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This is a rush transcript from "On the Record," June 19, 2012. This copy may not be in its final form and may be updated.

GRETA VAN SUSTEREN, FOX NEWS HOST: Tonight, Governor Mitt Romney says the media is wrong. Contrary to reports, the governor says Senator Marco Rubio is being vetted for the Republican ticket. So what does Senator Rubio have to say about a possible vice presidential run? We asked him.

(BEGIN VIDEOTAPE)

VAN SUSTEREN: Senator, nice to see you.

SEN. MARCO RUBIO, R-FLA.: Good to see you.

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    VAN SUSTEREN: Big day today. First the report this morning from ABC News that you were not on the vice -- not on the short list to be vice president for Governor Romney. Then by the end of the day, Governor Romney speaks out about this. He says, "Marco Rubio is being thoroughly vetted as part of our process."

    How's the day been?

    RUBIO: It's been an interesting day, yes. You know, look, I don't want to talk about the process. I haven't up to this point. It's Governor Romney's process and I want to be respectful of that.

    I think all of us should be -- all of us involved in politics should be respectful of this process because he has an important choice to make. He's going to make a great choice. I'm confident of that. And -- but I think out of respect for what he's going through and the process they're running through, I've just made a policy of not talking about it.

    VAN SUSTEREN: Would you concede it's been a little bit of a crazy day for you on this topic?

    RUBIO: Yes, well, you know, obviously, for the guys that work for me. I mean, we've been busy voting on the Senate floor and out there talking about our book. So obviously, you hear it from time to time. But look, it's just all part of the process. It's been, you know, quite an interesting ride around here the last few months, so...

    VAN SUSTEREN: Have you actually talked to the governor today?

    RUBIO: I have not.

    VAN SUSTEREN: OK. Now let me turn to the question of immigration. The president has signed an executive order about immigration for a certain segment of our society. You agree or disagree with what the president did?

    RUBIO: I don't agree with how he did it, that's for sure. And I want to say that I think there is a consensus, and I've talked about this with you and others, that we do want to help the young people who are undocumented through no fault of their own, have graduated high school, have very good grades, have a lot to contribute to the future.

    We have to help them in the right way. We also have an illegal immigration problem in this country, and it's a significant one. And so the balance we're trying to strike is, How do you help these kids who need the help but do it in a way that doesn't encourage illegal immigration? That's not an easy balance, but we have to get that right because otherwise, it could have some very significant unintended consequences.

    Unfortunately, the way the president's done this, there is no discussion. He's basically by fiat shoving this down the throat of the American people. And more importantly, he's ignoring the Constitution, ignoring the congressional process.

    I know I get frustrated with Congress, but that doesn't mean I'm about to ignore the republic because I have a really good idea that I think everybody else should see it the way I do. I think that's really the problem. From a practical point of view, what the president has done is going to make it harder for us to arrive at a reasonable bipartisan balanced approach to these kids' situation. And I think it is going to in the short-term I know a lot of these kids will be happy because they are desperate for a solution. But in the long term what they really need is a long-term solution. This is going to make it harder to find one.

    VAN SUSTEREN: Is the president signing the executive order, is it an unlawful exercise of power? Was it an unconstitutional move?

    RUBIO: I certainly think it ignores the constitution.

    VAN SUSTEREN: Are you saying sort of politely it was unconstitutional?

    RUBIO: Let me say the president believed it was unconstitutional not so long ago, and something changed in his mind. I think it was probably the proximity of the elections that he was willing to do something like this.

    VAN SUSTEREN: You are a lawyer. What do you think?

    RUBIO: I think it borders on unconstitutional. It's not that I don't want to tell you that it's unconstitutional, because I probably am going conclude that it is. But I think it is a strong statement, and before I say that I should study all of the applications of the law to make sure that is exactly the case.

    Let me put it this way. I think it ignores the constitution. I don't think it is constitutionally defensive. I think he had reached that conclusion. And I think I believe that after I'm he fully done analyze analyzing the situation I think all of us will arrive at the conclusion this is unconstitutional.

    VAN SUSTEREN: Do you think in the next two years regardless of who is president that we will finally have some definitive policy, immigration policy in this country, because right now some people are upset that the borders aren't being secure. Other people are upset because people are getting tossed out. There are people all over the board on this.

    RUBIO: I hope so, but this just made it harder because it poisoned the well and changed the dynamics this of. What is to stop the president now? Can he decide not to enforce the immigration law at all? And some argue that's exactly what he's done before we got to this point.

    This immigration issue is complicated. It is not an easy issue. On the one hand there is a real human element to it. The vast majority of people here undocumented are here because they are in search of a better life for their families. On the other hand we can't be the only country in the world that doesn't have immigration laws it enforces.

    And I think we also have to remind people we are the most generous country in the world on legal immigration. A million people a Europe immigrate to the United States legally. What other country in the world even comes close? And there are millions waiting to enter the country legally. They waited in line and paid the fees. What do we tell them -- come illegally, it is cheaper and faster? Those two things have to be balanced, and I think that is a hard thing to do and takes time to arrive that the point.

    But I think when he does these sorts of actions that ignore the constitution and ignore the Congress the president makes it harder for us to come together and work on the issue in a responsible way.

    VAN SUSTEREN: Senator, thank you, sir.

    RUBIO: Thank you.

    (END VIDEOTAPE)

    VAN SUSTEREN: Coming up, more of Senator Rubio. He has come under scrutiny about his family's journey from Cuba to America but says it was a blessing in disguise. What does he mean by that? Senator Rubio will be back and tell you.

    (COMMERCIAL BREAK)

    (NEWS BREAK)

    VAN SUSTEREN: Now, more with Florida senator Marco Rubio, and this time he is getting personal. He just wrote a new auto biography called "An American Son." We caught up with Senator Rubio on Capitol Hill.

    (BEGIN VIDEOTAPE)

    VAN SUSTEREN: Senator, it's always nice to see you. I love visiting your office.

    RUBIO: Yes. We are happy to be here.

    VAN SUSTEREN: And you have a new book out.

    RUBIO: I do, "An American Son," and we are very proud about it.

    VAN SUSTEREN: In reading your book, it is a very personal one. It's not about policy but more about you and your family.

    RUBIO: Yes. What I wanted to do is two things. One is tell our story because I think people could find insight and inspiration and maybe cautionary tales. And also I wanted to pay tribute to our country and through my family's story because I think what I want people to take from American son I is that that the reason I had the chance to do things that my grandfather and my father didn't have a chance to do is I was blessed to be an American son, to be born in this country where nobody really cared where I came from or where I was connected or wealthy. What they wanted to know are how good your ideas are and how hard you are willing to work. And so I think the best way to give life to that sentiment is kind of how it's played out in our family life.

    VAN SUSTEREN: I'll tell you a couple of things I took away from the book. One is there is a picture in the book of you signing papers running for the United States Senate with your father at your side. And we all have fathers. It is probably a huge occasion for your father. And then yet because of the laws of mortality he missed you winning the election.

    RUBIO: He unfortunately got sick that spring just a few weeks before that picture was taken. And so we -- in that event it was the qualifying event where you qualify to get on the ballot. And he lived long enough, and I talked about in the book tell the story about he tried to go to my victory party the night of the primary, which wasn't really in dispute. But he really tried that night to go to the victory party. My dad did everything he could to be there.

    I went by his house earlier that day and I found him, you know. My nephew answered the door and he was smiling and laughing. My father who probably hadn't been out of bed in probably a month and a half because he didn't respond well to chemo -- my father was standing up and sitting in his wheel chair but ready to go. The story was he wanted to go to the victory party that night. And unfortunately as the night got later it became impossible for him to do that. He wanted to make the one more sacrifice for us and be there.

    But, you know, I just have a feeling that he was there. Even though he wasn't there physically, I have a sense that he certainly knows what his hard work and sacrifice allowed me to do in my life.

    VAN SUSTEREN: You are a young man, but even as you write about in your book even in your journey so far there were times you were despondent about how you as a state legislator, worried about money and raising your family. You're making about $75,000 a year and had a wife and kids. And you use the word "despondent."

    RUBIO: There are people making a lot less that have a right to be even more despondent. Between the student loans and obviously the mortgage and car and all of that it starts to add up really fast. And I was afraid. I was at a point where I figured if I can't get this figured out in the next few weeks I will have to leave politics and find a job that pays more money, because one of the hard things about it was being in the legislature you had to find a boss or job that was willing to allow you to be gone for extended periods of time. And even then since that point I always as a provider for my family constantly had that in the back of my mind. And I think what it helps to do in addition to understand your own obligations, it helps you realize how many people are struggling and they make a lot less in some cases.

    VAN SUSTEREN: I guess the media is guilty of this but in some part it is true that the Republicans and Democrats clawing each other's eyes out up here, sort of scratching them out. But you write in your book about a Democrat, Senator Leahy pulling aside the young senator you and talking about family. I mean it is not quite as violent between the two parties. There are personal moments when you get advice isn't there?

    RUBIO: Senators act like normal human beings, especially when the cameras are not on them. Senator Leahy asked me how are things about and I mentioned I'm worried about my family and a not spending enough time with them and his expression changed. As I write in the book it changed to that of someone who had something to share. What he shared is the story that I end of book with about when was younger and in the Senate and I think President Ford invited him to something and he had to turn it dune because his kids had something. He said 30 years later he doesn't remember what the invitation was to, but his kids will never forget the day that he chose them over the president.

    I end with a chance I had to take a trip to Africa to learn about our aids program but my kids had a bunch of stuff going on and they were shocked when I went to school and picked them up. They thought I was halfway there. Maybe had I not written it in the book, I might have forgotten about that trip to Africa, but I don't think my kids will ever forget about the day I chose them over Africa and brought them home from school.

    VAN SUSTEREN: Some of the controversial issues in your career, you don't have many. You're lucky. But one is the issue about the air rents and when they were born and came to the United States. There is a new book written about you as well that talks about how that sort of experience about when your parents came to the United States. It has been a good experience for you personally because you went back and looked at your family.

    RUBIO: Obviously I knew the story. I didn't know the dates. It has been a blessing in disguise, because as part of the book and part of that scrutiny I went back and found ought as much as I could. And when you go back and can look at your parents, you end up realizing they were once my age. And that really comes alive when you review the documents and application to come to the U.S. and things of that nature. And I tried to capture some of that in the book. In some ways, in many ways the whole thing about when my parents came ended up being a blessing in disguise because it forced me to go back and learn everything I could about it. And what I learned was is even more amazing than what I knew before.

    VAN SUSTEREN: I assumed people get to where they are because they work hard and right place at the right time and a little bit of luck. In your instance I think the Governor Chris Christie hug of Obama.

    RUBIO: Governor Crist.

    VAN SUSTEREN: Governor Crist hug of President Obama, that was fatal to his campaign.

    RUBIO: It was -- it would have meant a lot less if it weren't the policies before that. Governor Crist is a very talented politician and a really likeable person. People like him. People and he was very success successful early on New Hampshire in his career as governor and very popular when I decided to run against him. The hug came in combination with a moment where a lot of people felt that the Republican Party was not clearly articulating what it stood for and being a forceful alternative to the president of this party. And that is one of the things that motivated me to run. So that is a tactic that we used. I think we would have won despite the hug.

    VAN SUSTEREN: But you were a long shot in the beginning.

    RUBIO: Absolutely.

    VAN SUSTEREN: Governor Crist had it locked up most people thought.

    RUBIO: His job approval ratings were very high, and he had the support that comes from being an incumbent, the money and all of that. As I talk about in the book, honestly, there were times I didn't think I could win and in fact was trying to figure out a face saving way to get out of the race. I'm glad that I didn't, but it's not a sentiment that I'm he proud of, but I'm glad to get out of that, because it forced me to ask why are you in this. If you are running to be somebody, there is a lot easier things you can be. Get into an easier race like attorney general or something else. Some people suggested I do that and I was tempted. Ultimately I ran because I wanted to do something. And I'm glad that I went through the race that I went through. It was difficult. It was uphill. I had doubts, because I think it made me hopefully a better or.

    VAN SUSTEREN: How close are you to Governor Jeb Bush?

    RUBIO: Close. He is a really good role model and someone whose opinions I value and someone whose advice has been important to my career, and someone who I think has issues first focus on policy is something I think is sorely missed in American politics.

    (END VIDEOTAPE)