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By Erik Ortiz

House Republicans unveiled their plan Monday night to dismantle and replace former President Barack Obama's signature health care achievement. But one key question remains unanswered: Just how much will this cost taxpayers?

Mick Mulvaney, director of the Office of Management and Budget, could offer no hard numbers for the GOP bill when asked Tuesday on TODAY.

"Everybody who’s looked at it knows this is going to save a dramatic amount of money," Mulvaney said, adding that the costs associated with the plan would be shared publicly before a congressional vote.

"Once you repeal the mandate in Obamacare, repeal the taxes in Obamacare, repeal the penalties in Obamacare and get out of that government-centric system, the [Congressional Budget Office] score is going to be very positive and helpful long-term to the deficit," Mulvaney said.

Related: Obamacare Lite? New GOP Health Care Bill Has Host of Critics

GOP leaders, including House Speaker Paul Ryan, are touting the legislation as a necessary replacement for the Affordable Care Act, and Mulvaney pledged it would give "everyone access to health care that they can actually afford."

President Donald Trump, who endorsed and ran on a platform to scrap Obamacare, tweeted Tuesday morning that the bill is now "out for review and negotiation."

Two House committees — Ways and Means and Energy and Commerce — plan to start reviewing the legislation this week. The bill must also move through the Budget and Rules committees before the full House can vote on it. Republican leaders say they want that to happen before Congress' spring break begins April 7.

A spokesperson for the Ways and Means Committee told NBC News it is a House rule that legislation must have a CBO score, which would indicate how much a bill would cost, on the way to the floor, but that the rule is sometimes waived if a score is unavailable.

Multiple top House Republican aides have said, as Mulvaney suggested, that there will be a CBO score before the replacement bill is voted on.

Related: Republicans Unveil Obamacare Replacement Bill

Aside from costs, it's also unclear how many Americans would potentially lose or gain insurance as a result of the new plan, although observers say the overall number of uninsured would likely rise if people aren't mandated to have insurance.

While Democrats have opposed repealing Obamacare, the Republicans' bill doesn't fully replace the law, which was signed by Obama in 2010 and covers about 20 million people.

The GOP plan provides a system of age-based tax credits to coax people to buy insurance in an open market as opposed to requiring Americans to have insurance or pay fines. The bill does keep some facets of Obamacare, including protecting patients with pre-existing conditions and allowing children under age 26 to stay on their parents' insurance.

Related: Obamacare Replacement Plan Faces Four Big Obstacles

"The program that we’ve talked about today that the House rolled out last night is a program that puts people in charge of their own coverage and they can go out and get that access through the safety nets and the other things that we are providing," said Mulvaney, who is helping with the launch of the bill along with Health and Human Service Secretary Tom Price.

But with details still needing to be ironed out and no previous public hearings on the bill, there are some Republicans who aren't happy with the revised plan, which also calls for freezing Medicaid expansion in the next four years.

In a tweet, Rep. Justin Amash, R-Mich., blasted the bill as "Obamacare 2.0."

Senate Finance Committee Chairman Orrin Hatch, R-Utah, also wouldn't rule out changes to the GOP plan in the Senate, where members have said they don't want to see more people without health insurance coverage.

"We have a right to look it over and see if we like it or don't," Hatch told reporters Monday.

Alex Moe and Hallie Jackson contributed.