The House approved a resolution Tuesday that would keep the government running through early April, even as dozens of Republicans signaled that they would no longer support short-term budget fixes.

On a 271 to 158 vote, the House approved a stopgap bill that would cut $6 billion from federal programs and keep the government open through April 8. Senate leaders in both parties have said they will pass the bill before Friday, when the measure that is currently funding the government expires.

The new temporary measure would be the sixth since the fiscal year began Oct. 1 and the second this month. It may also be the last, given the fraying support for short-term fixes among House Republicans, as well as from President Obama.

The 271 “aye” votes were 64 fewer than for the previous stopgap bill, confirming what many GOP leaders had said privately in the days leading up to the vote: Support for quick fixes is plummeting, and House Speaker John A. Boehner (R-Ohio), Senate Majority Leader Harry M. Reid (D-Nev.) and Obama have a three-week window to avoid a government shutdown.

“It’s very difficult to do more short-term” funding resolutions, House Majority Whip Kevin McCarthy (R-Calif.) said after the vote. “Who doesn’t know that?”

Fifty-four Republicans opposed Tuesday’s measure, a ninefold increase from the half-dozen who voted against the earlier two-week measure this month. Republican leaders were quick to note that many of the votes came after it was clear that the legislation would pass.

Boehner and Reid, however, remain far apart in their negotiations. House Republicans are standing by their proposal to slash $61 billion from this year’s budget and are demanding that Reid allow a full Senate debate to determine how deep the spending cuts would go in that chamber.

Reid has dismissed the Boehner bill as reckless and Tuesday reiterated his assertion that the speaker is being forced by tea-party-backed lawmakers into a showdown that could lead to a shutdown.

“We’re not going to take an ax to this budget,” Reid told reporters. “We’re going to work it as smoothly as we can and work to cut spending, but do it in a way that’s meaningful to the American people.”

Obama, who will leave later this week for a trip to Central America and South America, has remained largely detached from the negotiations, relying on aides and, once, Vice President Biden to try to nudge the talks along.

Complicating the effort to resolve this year’s budget are two upcoming events: the unveiling of the House Republican budget proposal for next year, with its politically perilous recommendations for entitlement reform; and the need for Congress to approve an increase in the federal debt limit.

Leaders in both chambers said they recognize that they must come to a resolution on this year’s budget so they can move on to battles over the 2012 budget and the debt ceiling.

“In all likelihood, as the House Republican leadership has indicated, we’ll then negotiate a final agreement for the balance of this fiscal year,” said Senate Minority Leader Mitch McConnell (R-Ky.).

Republicans also renewed their efforts Tuesday to frame budget cuts as a way to create jobs, despite the contention of many economic experts that much of the short-term impact of their proposals would include layoffs of federal and state employees.

On Tuesday, the top Republican on the congressional Joint Economic Committee issued a lengthy report arguing that cutting government spending will improve the economy. The report, released by Rep. Kevin Brady (Tex.), is based on academic studies of other countries showing that deficit-reduction plans that rely primarily on spending cuts lead to more robust economic growth than plans that rely heavily on new taxes.

However, the report acknowledges that the effect on short-term job creation is unclear. And it indicates that cuts to the government could depress wages in the private sector, noting that “a smaller government workforce increases the available supply of educated, skilled workers for private firms, thus lowering labor costs.”

Staff writer Lori Montgomery contributed to this report.