CNN  — 

Donald Trump is still one day away from taking the oath of office.

But on Capitol Hill, where Republican leaders have started the process of rolling back major parts of Obamacare and now face intense pressure to offer an alternative to the law as quickly as possible, the incoming president’s thoughts on the matter have quickly become a political liability.

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    Trump unexpectedly revealed over the weekend that his own plan to repeal and replace the Affordable Care Act was nearing completion, and promised that it would provide “insurance for everybody” – not to mention lower deductibles.

    Health care battle cheat sheet: Democrats vs. GOP

    Republican Sen. Orrin Hatch, the chairman of the Senate Finance Committee, bristled at Trump’s pledge to provide coverage for everyone, saying that it amounted to an overly ambitious promise.

    “It would be wonderful if we could do that. The problem is, is that you can’t do it and make overpromises on everything,” Hatch told CNN. “So we have to be very careful because there is a limit to what we can do.”

    Sen. Lamar Alexander, the top Republican on the Senate Health Committee and another key player in the GOP’s ongoing efforts to craft an Obamacare alternative, demurred when asked whether Trump’s promise for universal coverage was realistic.

    “We’ll just have to see what his plan is,” Alexander said. “I thought that was a very interesting observation and I’m going to wait until I actually see his plan in February – he may say other things between now and then.”

    Vice President-elect Mike Pence said Wednesday that a bill isn’t yet ready, but he’s “seen a lot of great ideas.”

    “It’s being crafted right now,” Pence said in an interview with CNN’s Dana Bash, when asked about a replacement to the President’s signature health care law. “We’re getting very close. We expect to have that plan come forward in the early days of the administration.”

    Democrats are more than happy to pit Trump’s recent statements against GOP lawmakers.

    When GOP Rep. Tom Price, Trump’s nominee for Health and Human Services secretary, testified before the Senate Health Committee on Wednesday, the panel’s top Democrat, Sen. Patty Murray, asked Price to answer to Trump’s words.

    “Just days ago, President-elect Trump promised ‘insurance for everybody,’” Murray said. “But Congressman Price, your own proposals would cause millions of people to lose coverage, force many to pay more for their care, and leave people with pre-existing conditions vulnerable to insurance companies rejecting them or charging them more.”

    Further frustrating GOP leaders is the fact that they have been kept out of the loop on the Trump transition team’s Obamacare proposal.

    Senate Majority Whip John Cornyn flatly answered “no” when asked this week whether he has been briefed by Trump officials.

    “I understand they are working on a plan, and we are eager to see it,” Cornyn said.

    Most conservatives have long opted to use the term “access” rather than “coverage” – a major fault line dividing Democrats and Republicans on the healthcare debate.

    To this end, Republican lawmakers have carefully avoided stating how many people could be covered under their revamped healthcare system – a rule that Trump flatly broke in his comments over the weekend.

    GOP Sen. John Hoeven pivoted to emphasizing “access” when asked about the idea of providing healthcare coverage to everyone.

    “We want to make sure everyone has access to coverage and we want to make it more affordable,” Hoeven told CNN.

    And Hoeven’s colleague, Republican Sen. Rob Portman, appeared eager to lower expectations when pressed by CNN multiple times on Trump’s comments.

    “I think we can do better than the current system, that’s the point,” Portman said.

    CNN’s Tami Luhby and Tom LoBianco contributed to this report.