The House will hold a vote on May 4 on a revised healthcare bill that Republicans hope will replace ObamaCare.
House Majority Leader Kevin McCarthy said the leadership in the party was confident it had secured enough votes for the bill to pass.
The bill would then go to the Senate where it could face a more tricky passage.
President Donald Trump made the repeal of Barack Obama’s signature law a central campaign promise.
The president has played a personal role this week in persuading wavering Republicans to come on board.
Their first attempt at getting a healthcare bill collapsed in disarray in March, despite the party controlling both legislative chambers and the White House.
However, several key Republicans this week reversed course, partly due to an amendment by Congressman Fred Upton to provide $8 billion over five years towards coverage for sick people.
But Democrats said the amount was woefully inadequate.
Senate minority leader Chuck Schumer said: “The Upton amendment is like administering cough medicine to someone with stage four cancer.”
Members of the House Freedom Caucus, a group of ultraconservative lawmakers, indicated the Upton amendment would not be a deal-breaker for them.
In March, the nonpartisan Congressional Budget Office said 24 million people would lose health insurance under the bill, which is called the American Health Care Act.
The bill has been amended several times as Republicans have tried to balance demands from opposing wings of their party.
Conservatives want to see a complete rollback of ObamaCare, while moderates are concerned about losing voters who like the existing law.
President Barack Obama’s overhaul of healthcare extended insurance coverage to millions of Americans, but some have experienced rising premiums in recent years.
One of ObamaCare’s popular elements is that it bans insurers from denying coverage to patients who are ill with “pre-existing conditions”.
President Donald Trump has insisted the revised bill will keep that, although it is thought that states will be able to opt out of making that an absolute provision.