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This is a rush transcript from "On the Record," January 24, 2013. This copy may not be in its final form and may be updated.

GRETA VAN SUSTEREN, FOX NEWS HOST: New Mexico governor Susana Martinez sticking to her guns, calling for a full repeal of a state law allowing illegal immigrants to obtain driver's licenses. The governor says she will continue to push for a repeal, even though state Democrats warn they will block it. But just one day earlier, Governor Martinez signaled a willingness to compromise with Democrats. She said she would consider legislation that creates a driver's permit for illegal immigrants. The permit could not be used, though, as identification.

Governor Martinez explains she will only consider other options if a full repeal fails.

And there are 11 million undocumented illegal people in this country. So why should the United States -- or what should the United States do about illegal immigration? We asked Florida senator Marco Rubio.

(BEGIN VIDEOTAPE)

VAN SUSTEREN: Senator, let me ask you a mixed question, one is on illegal immigration and the other is the future of the Republican Party, because there's a huge population out there, Hispanic population, and that's been a big issue.

SEN. MARCO RUBIO, R-FLA.: Well, two separate issues. I mean, illegal immigration is bad for America. Legal immigration is good for America. And the fact of the matter is that we have 11 million people in this country, more or less, that are undocumented. I don't know anyone who's happy about that. And -- but we have to deal with what we have. I mean, the truth is and the reality of is that these 11 million people, the vast majority are going to be here for the rest of their lives.

So I think our obligation as policy makers is to deal with them in a way that's compassionate and humane, but also responsible and in a way that's not unfair to anybody who has done it the right way and in a way that makes sure that we never have to do this again.

What I really he don't want to see is 10 years from now, we're back here talking about another 11 million people.

VAN SUSTEREN: What would you do with those 11 million people?

RUBIO: Well...

VAN SUSTEREN: I mean, there's got to be -- people say they don't want them to jump the line. They don't want to give them amnesty, they don't want to do all these things. But -- and they're going to be here forever, so what's your idea?

RUBIO: The outline is three-prong. The first, of course, is to modernize our legal immigration system. We need a legal immigration system that works better for our economy to work better, and by the way, to disincentivize illegal immigration. The second thing that we -- so we need to modernize the legal immigration system.

The second thing we need is and real enforcement. And it's just about fences and border security. That matters. We have to do that. It's about workplace enforcement. That is the ultimate enforcement mechanism is one that makes it impossible for someone who's here undocumented to get jobs.

And obviously, we also want to track when people enter and exit because about 40 percent of our illegal immigration is people that overstay visas. They come in legally and then they overstay.

And then the last part is, now you've got to deal with the 11 million people that are here. If you've committed any serious crime, you're going to be deported. Everybody else, what I think should happen is they should -- they should be given the opportunity to qualify for temporary, nonpermanent status, in essence, a work permit, if they pay back taxes, they pay a penalty, they have a background check that they can clear, et cetera. And they would have to be in that probationary period for reasonable but significant period of time.

VAN SUSTEREN: How are they going to pay those taxes? I mean, most of these people here illegally don't have jobs where they've been storing up a lot of cash to pay back taxes.

RUBIO: Well, there's just...

(CROSSTALK)

RUBIO: We're going to probably talk about that more in the next few weeks, but every plan that's out there has that element in it, and I think there's ways that we can accomplish that.

But moving forward, once they've been in this probationary phase for some period of time, at that point, the only thing that they would get is the opportunity to basically apply for the existing legal immigration system, just like anybody in the world would. In essence, they'd have to identify a visa they want to apply for, they'd have to get in line and wait until it's their turn behind everybody who applied before them. And when their turn came, they'd have to qualify for that visa. And then what they get is a green card. And then they've still have to wait another five years just to apply for citizenship.

So, you know, at that point, all you're basically doing, the best way to understand it, giving folks qualified, that are undocumented, the opportunity to act, to gain a work permit and then in the eventually, the opportunity to apply for a legal immigrant visa in the same way anybody in the world would do. No special way.

VAN SUSTEREN: All right, the Republican Party, obviously, they need to do some revamping of some sort. And I'm curious, what would you do to attract more people to -- I mean, so that people didn't -- so that people who are currently moderates or Democrats or independents that they want to be a Republican?.

RUBIO: The fundamental desire of all Americans from all walks of life, including Americans of Hispanic descent, is to get ahead in the middle class and leave your children better off than yourself. And I think that free enterprise and limited government is the best way to accomplish that.

So I think we have the right principles. We just have to do a better job of selling them to people and explaining to the people and to be true to those things, too. I mean, I don't think we should be more Democrat than the Democrats. I think that to some, we can do a better job of selling what we stand for and explaining to people what we stand for and why what we believe in is better for them and for their hopes and dreams than what the Democrats are offering.

VAN SUSTEREN: Suppose you're thinking about Social Security and you're a Democrat and thinking here the Republicans want to revamp it they say it's not going to last, that it's not sustainable, but the Democrats say, yes, it is. Why would you switch to be a Republican, why would you switch? Why would you buy that?

RUBIO: Because I think that people understand math when you explain this is how much money comes in, this is how much goes out, and as a result this is the year we run out of money unless we do a few simple and important things, people understand that.

VAN SUSTEREN: I'm here -- I'm here, I'm a Republican I'm here to help you, believe my math?

RUBIO: People understand that. At the end of the day I don't think we give the American people enough credit for their ability to understand the complexity of an issue and to have leaders to explain it to them and that explain their options to them. Ultimately we're going to pay a price if the issues are not resolved. And Medicare is a much, is an even more dangerous situation because it runs out of money sooner than Social Security does in regards to this.

But ultimately that's what leadership is about. Leadership is not just about winning elections or hitting the 65 percent issues in the polls. Leadership is about going to the people you represent and telling them the truth, whether it's a convenient truth or not, and explaining to them these are our options and this is the one I think is the best one moving forward for our country and for you.

And then ultimately in a republic people decide whether they want to support that or not, and then the country faces the consequences of the decision made or not made.

VAN SUSTEREN: Do you get frustrated sometimes?

RUBIO: Not really. More frustrating is to be in a country where you wouldn't be able to debate the issues and have a chance to go to people and explain what you stand for or you worry about speaking your mind because you could be put in jail by the governing party. So I'm grateful I live in a republic in what I believe is still the greatest country in the history of the world.

VAN SUSTEREN: Senator, nice to see you.

RUBIO: Thank you.

(END VIDEOTAPE)