House Majority Leader Kevin McCarthy said the leadership in the party is confident it has secured enough votes for the bill to pass.
It would then go to the Senate where it could face a more tricky passage.
President Donald Trump made the repeal of his predecessor’s signature law a central campaign promise.
He 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.
But several key Republicans this week reversed course, partly due to an amendment by Congressman Fred Upton to provide $8bn (£6.2bn) 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.