WASHINGTON — After a marathon session of voting on budget bill amendments, Senate leaders failed Friday to bring up a vote on a potentially groundbreaking compromise to fix Medicare’s system for paying doctors and to extend funding for a popular government health insurance program for children.

The inaction means Medicare will start processing a 21 percent cut in fees to physicians on Wednesday, though the reduced payments will not start hitting medical offices until the middle of next month. Senators, meanwhile, will have to take up the stalled health care package after they return from their two-week recess on April 13, one day before doctors will start to see the effects of the cut.

Senate Majority Leader Mitch McConnell, R-Ky., who could not persuade a few lawmakers to drop their opposition to quick action on the bill, expressed confidence early Friday that the Senate would act quickly when it returned.

The legislation, which was negotiated by senior House Republicans and Democrats, won strong bipartisan support in the House, passing 392 to 37 on Thursday.

President Barack Obama has said he will sign the bill, which drew support from dozens of influential interest groups on the left and right, despite lingering opposition to parts of the package from some parties.

Medical groups called on senators not to delay further.