The budget panel, voting 19-17, passed the American Health Care Act, which now heads to the House Rules Committee.
"We did not encourage them to vote 'no,'" Freedom Caucus Chairman Mark Meadows, R-N.C., told reporters Thursday afternoon. "Our members have unbelievable resolve in making sure this bill gets changes so it helps their constituencies back home."
The House GOP leadership and the White House are working hard to sell the measure to both conservatives and moderates in the party, who have different sets of concerns about the bill. With Democrats expected to vote as a bloc against the legislation, Republicans can afford to lose no more than 21 votes to pass the bill in the House.
"I'm a very strong man of faith, but I think if St. Peter called and said, 'You need to vote for this bill to get to heaven,' I'd say, 'St. Peter, I can't do it,'" Rep. Walter Jones, R-N.C., told reporters Thursday when asked how he would vote on the bill.
He said he thinks legislators are moving too fast on the health care plan.
House GOP moderates are in general concerned about the bill's restrictions on federal Medicaid funds and the likelihood that the legislation won't pass the Senate, where Republicans from states that expanded Medicaid coverage under Obamacare have also signaled opposition to the bill's changes to the program.
Among Republican conservatives in the House, primary concerns include the proposal's refundable tax credits, its effectiveness in lowering insurance premiums and its slowness in making changes to Medicaid.
"We're making refinements based upon the feedback we're getting from our members," he said in a news conference Thursday. "The goal here is get to a bill that ... we can pass and that is actually great policy, and the president is playing a very constructive role on this."
The bill will likely require significant revisions in the Senate, where Republicans can afford to lose only three GOP votes. Conservative senators have also objected to several provisions.
The House Rules Committee will take up two additional health-care-related bills next week as part of the planned health care overhaul that Republicans are moving through Congress. Those bills will require at least 60 votes to clear the Senate.