WASHINGTON — After seven years of waiting longingly to annul President Barack Obama’s signature health care law, Republican leaders on Tuesday faced a sudden revolt from the right that threatened their proposal to remake the American health care system.

The much-anticipated House plan to repeal the Affordable Care Act also drew skepticism from some of the party’s more moderate members, whose constituents have benefited from expanded coverage in recent years.

The criticism came even before lawmakers knew the cost of the replacement plan and how many people might lose their health care if it were enacted.

House Republicans were rushing the legislation through two powerful committees — Ways and Means, and Energy and Commerce — with the hope of a full House vote next week, an extraordinarily compressed time frame considering that the legislation affects many parts of the United States economy and could alter the health care of millions of Americans.