WASHINGTON — After a sweeping vote by conservative Republicans controlling the House and President Obama’s Democratic allies, a bipartisan budget pact is in the hands of the Senate, where it will encounter stronger but probably futile resistance from Republicans.

The modest package passed by the House on Thursday would ease the harshest effects of another round of automatic spending cuts set to hit the Pentagon and domestic agencies next month. Supporters of the measure easily beat back attacks on it from conservative organizations that sometimes raise money by stoking conflict within the Republican Party.

At the same time, Democrats who were upset that the bill would not extend jobless benefits for the long-term unemployed suppressed their doubts to advance the measure to the Democratic-led Senate, where Obama’s allies appear set to clear it next week for his signature.

Senate Democrats promise to force a vote on extending unemployment benefits when the chamber reconvenes next year. They hope that political pressure after 1.3 million people lose their benefits on Dec. 28 will force GOP leaders to knuckle under and extend aid averaging under $300 a week to people who have been out of work longer than six months.

The bipartisan bill breezed through the House on a 332-94 vote, with lopsided majorities of Republicans and Democrats alike voting in favor.

Thursday’s vote was a big win for House Speaker John Boehner, R-Ohio, who earlier in the day lobbed another salvo at conservative interest groups that attack Republicans for supporting legislation they deem not conservative enough.

Republican Sen. Marco Rubio of Florida criticized the deal, saying, “I mean, compromise just for the sake of compromise, so we can feel good about each other, I don’t think is progress for the country.”

The measure leaves in place the bulk of $1 trillion or so in automatic cuts slamming the Pentagon, domestic agencies and Medicare providers through 2021 but eases an especially harsh set of cuts for 2014 and 2015.

The cuts would be replaced with money from, among other things, higher airline security fees, curbs on the pension benefits of new federal workers or working-age military retirees and premium increases on companies whose pension plans are insured by the federal government.

The Ryan-Murray pact uses a combination of mostly low-profile cuts and new fee revenues, much of which won’t occur until after the turn of the next decade, to ease cuts mandated by the inability of official Washington to follow up a 2011 budget pact with additional deficit cuts.

Those cuts were intended to be so fearsome that they would force the capital’s warring factions to make budget peace. Instead, after the first-year impact of so-called sequestration wasn’t as bad as advertised, many Republicans have come to embrace them. The Ryan-Murray deal recognizes that the second year of the automatic cuts would be worse than the first, especially for the Pentagon, and seeks to ease their pain.

Thursday marked the second consecutive day that Boehner went on the attack against conservative groups like Heritage Action, the Club for Growth and the Senate Conservatives Fund, which often raise money by attacking the GOP establishment.

“They pushed us into the fight to defund Obamacare and shut down the government,” Boehner said. “That wasn’t exactly the strategy I had in mind. But if you recall, the day before the government reopened, one of these groups stood up and said, ‘Well, we never really thought it would work.’

“Are you kidding me?”

Rubio, who is considered a potential GOP presidential contender and is supported by those groups, said Friday, “Look, I think outside groups have a right to express their views.”

Associated Press writer Henry C. Jackson contributed to this report.