The measure would buy additional time for talks between Capitol Hill Republicans and the Obama administration on a bill to fund the day-to-day operations of the government through the end of September. Those negotiations haven't gotten very far yet and House GOP leaders haven't shown much flexibility.
The measure passed by a 271-158 vote. The $6 billion cut by the measure includes many items that the Obama administration and Democrats agree can be axed.
Fifty-four Republicans opposed the bill, which meant that Democratic support was required to pass it - a prospect that GOP leaders must avoid to keep control of the debate in future rounds.
"It's a small down payment on our commitment to the American people that we'd have real fiscal responsibility," said House Speaker John Boehner, R-Ohio.
The measure moves to the Senate, which is likely to clear it for Obama's desk later this week. White House Press Secretary Jay Carney said in a statement after the vote that Obama supports the bill but signaled the White House is impatient with the lack of progress on a final measure.
"With the wide range of issues facing our nation, we cannot keep funding the government in two- or three-week increments," Carney said. "It is time for us to resolve this issue in a sensible way."
Prospects for agreement on a longer-term measure remain uncertain. Republicans dominating the House are insistent on a measure mixing steep spending cuts with numerous policy provisions. Provisions include a ban on federal funding for Planned Parenthood, a measure to strike money to bankroll implementation of Obama's signature health care law, as well as language to block the Environmental Protection Agency from regulating emissions believed to contribute to global warming.
Those policy riders are strongly opposed by Democrats and Obama and are likely to be at the center of any impasse that leads to a partial government shutdown.
"They are using the budget to try and shoot the moon on a wish list of far-right policy measures. If this debate were about spending cuts we could probably come to an agreement before too long," said Sen. Charles Schumer, D-N.Y. "We do not want any of these controversial riders to be in the bill. That's the bottom line."