WASHINGTON — The Republican-led House of Representatives has been relentless this week in its determination to chop billions from domestic programs.

While it’s been a messy process, there are signs that unlike past bids, this one could succeed at least partially. This week marks the first time in years that lawmakers have been voting consistently to shrink government, even if it means angering constituents and bucking their leaders.

The House, where Republicans outnumber Democrats 241-193, approved a spending package early Saturday that would cut more than $60 billion over the next seven months. The vote was 235-189, with no Democrats voting for it and only three Republicans opposing it. The measure would severely pare such programs as job training and employment grants, community health centers, high-speed rail, diplomatic programs, the Corporation for Public Broadcasting and more.

That meat-ax approach is certain to be diluted in the Senate, where Democrats control 53 of the 100 seats, and President Barack Obama already has threatened to veto the House measure should it reach his desk.

But House Republicans are still expected to have a strong voice in crafting the final package in negotiations with the Senate, and Democrats agree that some cuts are necessary. In fact, Obama’s own new budget targets many of the same programs for cuts.

“”Eventually a grand compromise will emerge,”” said Lee Hamilton, a former Democratic congressman and now director of the Center on Congress at Indiana University.

The most telling vote this week came Wednesday when the House voted to cut $450 million and kill development of a second engine for the F-35 Joint Strike Fighter. For years Congress has backed development of the General Electric-Rolls Royce engine — whose contracts are spread far and wide around the country, winning support from many members of Congress — but Wednesday 47 of the 87 Republican freshmen opposed it. So did 19 Democrats and 13 Republicans who voted for funding the engine last year.

House Speaker John Boehner has long supported the project, since it created hundreds of jobs in his southern Ohio district, and he opposed the vote to kill it. But he shrugged Thursday, saying the vote was simply the House “”working its will.””

That vote illustrates how the rules of budgeting are changing, as many lawmakers are willing to buck their leaders — and their constituents’ narrow interests — for the greater cause of cutting spending and shrinking government.

This year’s budget deficit is expected to reach a record $1.65 trillion, and the national debt is skyrocketing. Republicans won election in November on a pledge to make tough fiscal choices.

“”In many ways, the tea party has already made tremendous progress,”” said Burdett Loomis, a congressional expert at the University of Kansas.

Not only are GOP freshmen determined to act, but veteran conservatives have waited years to enact changes on the scale they’ve proposed this week.

“”For four years, my colleagues have not been able to offer a lot of changes,”” said Rep. Jeff Flake, R-Ariz. From 2007 through January, when Speaker Nancy Pelosi was in charge, conservatives rarely were allowed to amend spending bills.

Also driving the Republicans’ resolve is fear of the political future. Several incumbent Republicans lost nominating contests last year to tea party insurgents, and another round of primaries and party conventions are barely a year away.

“”We all remember we made promises on spending,”” said Rep. Mike Simpson, R-Idaho.

Federal spending authority expires March 4. If no plan is enacted to fund the government beyond that date, the government will shut down. Few anticipate that happening; many are talking about extending the deadline with short-term stopgap spending bills while talks continue. But Boehner said Thursday that even a short-term extension had to include some cuts.

Once the fiscal 2011 budget is resolved, attention will turn to the broader task of writing a budget for fiscal 2012, which begins Oct. 1, and beyond.

House Republicans feel energized by this week’s action, and they want strong signs from Obama himself that he’ll buy some of their cuts. “”We need his leadership,”” said Rep. Wally Herger, R-Calif.

Republicans also want leadership from Boehner.

His open-amendment process, which resulted in 583 amendments being offered, often looked chaotic. Historically, tax and spending bills are considered under rules that strictly limit debate and amendments.

Analysts think that eventually the leaders will convince conservatives to swallow some compromise.

“”John Boehner and (House Majority Leader Eric) Cantor are not naive,”” said Loomis. “”You’ll see tightening up.””

But maybe not as tight as in the past, not after this week’s success, and not with bloggers, tweeters and e-mail available to remind new lawmakers of their mandate.

“”I’m not certain what’s going to happen,”” said former Congressional Budget Office Director Rudolph Penner, now a senior fellow at Washington’s Urban Institute. “”A lot of people have to worry about what’s going to happen in those primaries.””