Updated

This is a rush transcript from "Your World," June 28, 2017. This copy may not be in its final form and may be updated.

NEIL CAVUTO, HOST: Now to RNC Chair Ronna McDaniel, who has a good sense of humor about these sort of things and patience as well.

Ronna, very good to have you. Thanks for coming.

RONNA ROMNEY MCDANIEL, CHAIR, REPUBLICAN NATIONAL COMMITTEE: Well, thanks for having me, Neil.

CAVUTO: All right, let's talk a little bit about John Thune and what he outlined and what Republicans want to do, get something out there by Friday that obviously woos more senators and gets a better kind of a read from the CBO before July 4, so, soon afterwards, they can vote on that.

Aggressive timetable? Doable? What do you think?

ROMNEY MCDANIEL: Oh, I think it's doable. I was with many of the senators yesterday.

There's a sincere effort among the Senate to get this ball rolling. And there's a recognition that people are really hurting, and they're looking to Republicans right now to help bring relief to people whose premiums are going up, who have insurance agencies pulling out of their marketplaces.

This is a real problem. So, we have to get this done. It's something we ran on. We have majority in the Senate, and the House and the White House, and we have to deliver.

CAVUTO: How much do Republicans pay attention -- and there are more protests, for example, around on Capitol Hill today. Again, the argument being that Republicans are out to destroy health care, kill hundreds of thousands of people.

I mean, how do you counter these arguments that many in the press people don't even try to check, challenge, fact-check, you name it?

ROMNEY MCDANIEL: Well, I think we always have to remember the evolution of how we got here.

It was the Democrats passing a bill, 30,000 pages of legislation, with no Republican input. They said you can keep your doctor. Many people couldn't keep their doctor. They said you can keep your plan. That hasn't happened. Premiums have risen. They said it was going to be affordable.

And now you have insurance companies pulling out of marketplaces. ObamaCare is failing. And we got here because Democrats put something in place that was not sustainable, probably with the hope that we would end up with a single-payer system.

CAVUTO: So, how do you feel that -- you're right about citing all these problems with the Affordable Care Act that it's not affordable, it's that falling of its own weight just mathematically.

But yet Republicans and their plan has an even lower approval rating, only 17 percent. How did that happen? How do you counter that?

ROMNEY MCDANIEL: Well, the plan is not fully out there yet. But what voters need to know is, Republicans are working to make sure that the patient-doctor relationship is restored. We want to put coverage closer to the voters, closer to the patients.

CAVUTO: But they're not getting that message. They're not getting that message.

So I'm wondering, like, what do you do to counter it?

ROMNEY MCDANIEL: Well, I come on your show. And we have to talk about it and we have to get that out there.

CAVUTO: Good move.

ROMNEY MCDANIEL: I mean, voters need to know that Republicans are working hard to solve this problem. Democrats are sitting on the sidelines.

They helped -- they created this problem, and they're not helping. But we recognize that people are looking for relief. Part of the reason we were elected is because people were hurting. I see it all the time. I go home to Michigan. I run into people. They say my premiums have doubled. My deductibles are so high. I may have health insurance, but I don't have health care. I'm afraid right now. I'm making choices between, do I pay my health insurance or do I pay for rent?

CAVUTO: They're not the only ones, right? They're not the only ones. The money guys, the people who fuel the Republican Party, are they getting nervous? Or are they holding off until this is resolved?

I know the president will have a big fund-raiser tonight just down the street in Washington. And he's had no problem raising money, period. But do you worry that this is going to cause some to sit on their hands until they see more legislative wins here?

ROMNEY MCDANIEL: I think Republicans are focused solely on the people who are hurting right now, who recognize that the system is collapsing, that people in the near future are not going to have any choice in the marketplace.

We have seen these states where they have one insurer left. Premiums are going to go up by in some cases up to 43 percent. It's not sustainable for a family to have suddenly 200 more dollars added to their monthly bill. They can't do it.

We have to find relief for these families. They elected us to do it. It would be great if Democrats would come along and help. It would be great if we could find a way to work together and not make this a political football.

It's unfortunate that Democrats have no interest in solving a problem they created. But Republicans are committed to it. We recognize the urgency. We recognize that people are looking to us to find relief. And, right now, they're working together do it.

CAVUTO: Well, do you think the president should get more involved then? He's a pretty effective communicator in his own right? Do you think he should be ringleading his effort? Does he want to? What are people saying?

ROMNEY MCDANIEL: The president -- yes, by having the senators over at the White House yesterday, I mean, that was amazing, for the president to say, come and sit with me. And he's having conversations.

The president heard it. He was in states like Michigan, and Wisconsin, and Iowa. He was all over this country. He saw this firsthand, the suffering that is happening because of ObamaCare.

CAVUTO: But he also said of the first attempt at this on the part of the House that it was mean. Now, I know what he meant, stepping back from it here. So, he doesn't want a mean measure, which can easily be interpreted by some that he wants one that could be a tad more expensive.

Do you subscribe to that?

ROMNEY MCDANIEL: Well, there's a balance. There's a balance.

The plans that are coming forward do you allow preexisting to stay -- preexisting condition to stay on insurance. They allow for children up to 26 to stay on their parents' insurance. I shouldn't say children. Adults up to 26 to stay on their parents' assurance -- insurance.

All of these things we have to do, we wanted to have a transition, so that the people are not hurt as this transition takes place from a failing health care system to one that is sustainable that will actually restore patient-doctor relationship, that will bring down premiums and bring health care closer to the people.

CAVUTO: So, if this doesn't work out -- and I know you're optimistic that it will -- would you start to worry? Would you start to say, as many in the markets worry, today notwithstanding, that the agenda itself could be compromised?

ROMNEY MCDANIEL: Well, I would worry if this doesn't work out because ObamaCare is failing and collapsing. I don't think not finding a solution is an option. We have to put something out there that is going to help these people.

CAVUTO: All right, Ronna McDaniel, thank you very much.

She's the RNC chairwoman.

Very good having you again. Thank you.

ROMNEY MCDANIEL: Thanks for having me, Neil.

CAVUTO: All right.

END

Content and Programming Copyright 2017 Fox News Network, LLC. ALL RIGHTS RESERVED. Copyright 2017 CQ-Roll Call, Inc. All materials herein are protected by United States copyright law and may not be reproduced, distributed, transmitted, displayed, published or broadcast without the prior written permission of CQ-Roll Call. You may not alter or remove any trademark, copyright or other notice from copies of the content.