WASHINGTON — No one will be adversely affected by the Republicans' new health care bill once it's enacted and more people would be covered, according to Health and Human Services Secretary Tom Price.

“I firmly believe that nobody will be worse off financially in the process that we're going through," Price insisted when pressed by NBC’s Chuck Todd during Sunday's “Meet The Press.” "They'll have choices that they can select the kind of coverage that they want for themselves and for their family, not the government forces them to buy."

“There's cost that needs to come down, and we believe we're going to be able to do that through this system,” he added. “There's coverage that's going to go up.”

Later on "Meet The Press," former Health and Human Services Secretary Kathleen Sebelius rejected Price's assertion that more people would get health care coverage under this new proposal.

"There is no estimate looking at this bill that with less money going to subsidies, with older Americans being able to be charged five times what younger Americans are being charged, and with no variation based on income that more people will have coverage," she said.

Price, a former doctor who has been in his new position for just over a month, was previously a Republican congressman from Georgia. A longtime opponent of Obamacare, he is now leading the Trump administration’s quest to repeal and replace one of the former president's signature initiatives.

The effort has caused a political firestorm.

This week, House Republicans unveiled a new health care bill called the American Health Care Act, which has been referred to as "Trumpcare" and scraps Obamacare’s individual mandate. It replaces subsidies that low-income people can use to buy insurance with limited tax credits, and freezes the Medicaid expansion program over the next few years.

Related: The GOP Wants More Health Care Choices. Is That Really a Good Idea?

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President Trump has supported the bill, but has also tweeted that it was out for “review and negotiation.”

"We strongly support the plan, which is this bill," Price said on “Meet The Press."

The bill has its share of critics, from Democrats concerned about the undoing of the Affordable Care Act, to some Republican governors and senators defensive of their state’s Medicaid expansions, to other conservative Republicans dubbing it “Obamacare 2.0” (like Justin Amash) or “Obamacare Lite” (like Rand Paul).

The House bill is “absolutely not” “Obamacare Lite,” Price said.

“This is a little puzzling because independents and conservatives for decades have said, ‘Shouldn't we equalize the tax treatment of the purchase of health coverage for folks who get it through their employer and folks who aren't able to get it through their employer?’" he said.

He added: "That's exactly what the tax credits do. We don't dictate to people what they ought to buy or what they must buy.”

"I'm not sure what the goal is here," Sebelius said of the House bill. "So they have kept some pieces. The preexisting conditions. They have kept some subsidies but I would say in sort of the wrong place to the wrong folks."

Asked why they don’t means test the tax credits instead of applying them by age, Price responded that “there's an opportunity to put some means testing in there but that's not the correlation factor to what it actually costs. Age is the thing that correlates best to what health coverage costs.”

The bill’s cost is still unclear, and the Congressional Budget Office has yet to declare a price estimate. But external organizations have weighed in, including the Brookings Institution, which estimated that “at least 15 million people will lose coverage under the American Health Care Act (AHCA) by the end of the ten-year scoring window.”

Price rejected that assertion.

“I'll tell you that the plan that we've laid out here will not leave that number of individuals uncovered. In fact I believe, again, that we'll have more individuals covered,” he said.

An analysis from the Kaiser Family Foundation also found that the bill would broadly offer less help to Americans living in rural areas, as well as older people and those on lower incomes. According to Kaiser estimates, a 60-year-old making $30,000 a year would receive a $4,000 tax credit under the AHCA — nearly $8,000 less than what he or she would receive under Obamacare.

Price claimed that analysis is “looking at it in a silo.”

“If you look at it in the way that the market will allow, then, for individuals to have choices, who knows what that 60-year-old wants?” he asked.

The secretary declined to offer a specific number for what the administration would use to define this legislation as a success.

But he responded more broadly, saying success would be “more people covered than are covered right now, and at an average cost that is less. And I believe we can firmly do that with the plan that we've laid out there.”

Sebelius, for her part, did acknowledge that there's room to improve the current health care system under the Affordable Care Act, responding to former President Bill Clinton's line on the campaign trail calling part of the situation for people now "the craziest thing in the world."

"He does have a point," she said. "There is a cliff. It was set in this bill as 400 percent of poverty. And then you don't any longer have a subsidy. In the marketplace right now, about 85 percent of the folks have a subsidy. So every talk about premium increases, that isn't what consumers are paying because actually their subsidies rise with the premiums' rise. Again, this is fixable. You could have a much more graduated subsidy system. You could have a higher income point. That could easily be done to stabilize the marketplace. But that wasn't what the Republican Congress wanted to do. They wanted to actually dismantle this bill from the outset."