The contentious plan, opposed by all Democrats and some fiercely critical Republicans, narrowly survived a vote in the House of Representatives Budget Committee.
Two conservative Republicans on the panel opposed the measure but it was not enough to block the plan, which advanced on a 19-17 vote.
House Speaker Paul Ryan, who along with President Donald Trump is a champion of the plan that rolls back several existing health insurance provisions, has said he hopes the bill will come up for a full floor vote next week.
But the top Republican in Congress acknowledged criticism of the plan from within his own party has made it likely that the bill will undergo some form of revision so it can get across the finish line in the House and Senate.
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"We're working at bridging those gaps to make improvements to the bill," Ryan said.
If 22 of the House's 237 Republicans vote no, and Democrats are united in opposition, the health care bill will fail.
Staunch conservatives sharply criticize the measure because its tax credits for Americans to buy insurance are too similar to the subsidies provided under Barack Obama's health care law.