"We'd better be sure that we're prepared to live with the market we've created" said Rep. Tom McClintock, R-Calif., according to the Washington Post. "That's going to be called Trumpcare. Republicans will own that lock, stock and barrel, and we'll be judged in the election less than two years away."

Sen. Rob Portman, R-Ohio, a relative moderate, also predicted that the hundreds of billions of dollars that Republicans have promised to save by repealing the ACA would in fact be poured into setting up a replacement program.

Rep. Pete Sessions, R-Texas, expressed concerns about a slimmed-down plan that focuses on giving people tax credits to buy insurance. Echoing arguments made by Democrats, Sessions said such a plan would likely not be enough to provide coverage for financially-strapped families.

"We're telling those people that we're not going to pull the rug out from under them, and if we do this too fast, we are in fact going to pull the rug out from under them," said Rep. Tom MacArthur, R-N.J., speaking in particular about the Medicaid expansion that is linked to coverage for roughly 11 million.

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Some conservative hardliners, however, don't share their colleagues' anxieties.

"Getting ahold of the Medicaid expansion and repealing that is absolutely critical if we're going to have control of the growth of entitlement spending," said Rep. Bob Goodlatte, R-Va., who later added states which did not embrace the expansion "want to be proven that they were right originally."

The GOP's anxiety about Obamacare comes on the heels of polls showing higher support for the law since Trump's election. A recent poll conducted by the Associated Press-NORC Center finds 56 percent of Americans are concerned about repeal could lead to a major loss in coverage.