WASHINGTON — A $1.1 trillion spending bill for operating the government until just before next fall’s election steamed through the battle-weary House on Wednesday over tepid protests from tea party conservatives, driven by a bipartisan desire to restore painful cuts in domestic and defense programs and show disaffected voters that Congress can do its job.

The bill swept through the House on a 359-67 vote and was on track for a big Senate vote by week’s end. Republicans voted for the bill by a 2½-1 margin, and just three Democrats were opposed. Sen. Mike Kelly, R-3rd, voted for the bill.

The measure funds virtually every agency of government and contains compromises on almost every one of its 1,582 pages. It covers the one-third of government spending subject to annual decisions by Congress and the White House, programs that have absorbed the brunt of budget cuts racked up since Republicans reclaimed control of the House three years ago.

Excluded are the giant benefit programs like Social Security, Medicare, Medicaid and food stamps that run on autopilot and are increasingly driving the government deeper into debt.

Tea party Republicans, chastened after sparking a 16-day partial shutdown of the government, appeared resigned to the bill.

“I don’t think there’s going to be a lot of opposition,” one tea party leader, Rep. Raul Labrador, R-Idaho, said before the vote. “The die has been cast for the next year on budget fights.”

To buy time for the Senate debate, Congress on Wednesday sent President Barack Obama a three-day funding bill in time to avert a scheduled shutdown at midnight. The Senate cleared that measure by an 86-14 vote.