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“We would like those cuts to come from someone … who has done well the last couple of years,” said Rep. Jane Harman, California Democrat.

Under the deal between liberal and conservative Democrats, liberal members also won an agreement to hold a floor vote on establishing a single-payer health care system when the House returns in September. The single-payer system, used in Canada, was never seen as politically viable and was not given serious consideration in the Congress until now.

The Blue Dogs, who held the balance of power in light of near-universal Republican opposition, had threatened to vote against the bill in committee unless the structure of the public plan was changed and more cost-cutting measures were introduced.

Progressives balked at a deal between the Blue Dogs and Mr. Waxman earlier this week that would have eliminated $100 billion in subsidies over the next decade. The new plan would restore to the bill about $50 billion, which would be put back into the plan as subsidies for low-income people, said Rep. Tammy Baldwin, Wisconsin Democrat.

The markup ended late Friday night with about 60 outstanding amendments, according to Mr. Waxman. The remaining amendments will be considered under a separate bill in September, under an agreement between Mr. Waxman and ranking member Rep. Joe L. Barton of Texas.