Washington (CNN) The House approved a one-week extension of funding for the Department of Homeland Security, avoiding a partial shutdown just hours before a Friday night deadline.

President Barack Obama signed the bill, which funds the Department of Homeland Security until March 6.

The bill does nothing to resolve the central issue that has turned the agency's funding into a political football: immigration. Republicans will again push to tie money for DHS to legislation rolling back Obama's immigration orders. Senate Democrats will block that effort, ensuring another tumultuous week on Capitol Hill and more uncertainty for the hundreds of thousands of people who work at DHS.

There was already plenty of drama in Congress on Friday. Earlier in the day, the House rejected a bill that would have kept DHS open for three weeks, a shocking twist that renewed questions about Speaker John Boehner's grip on the House.

Rep. Steve Womack, R-Arkansas, who is close to House leadership, described House Speaker John Boehner's situation as like a "vice."

'Hell of a position'

"It's a hell of a position to be in," Womack said Friday evening. "I just can't imagine the frustration the speaker must have now."

Two senior House Republican sources tell CNN there was serious concern among those close to the Speaker that if he allowed a vote on a clean DHS funding bill without immigration language, conservatives would make a motion to vacate the chair, which amounts to a direct challenge to his job.

Pennsylvania GOP Rep. Charlie Dent acknowledged to reporters he heard conservatives were using the DHS fight to try to remove Boehner.

"Right now, we have to get serious," he said. "I think a lot of people better get serious about governing and it's time for all of these, you know, DC games to end. I mean all these palace coups or whatever the hell is going on around here has to end, and we have to get down to the business of governing."

The battle over DHS funding comes more than 16 months after political chaos tipped the entire government into a shutdown. Republicans bore the brunt of the public's blame for that episode and polls indicate the party would be blasted again.

A CNN poll last week found 53% of Americans would blame Republicans in Congress if the department shuts down, while 30% would blame Obama. Another 13% said both would deserve the blame.

Boehner has been here before -- wedged between his hard-right flank and the Senate. House conservatives want to continue fighting to block Obama's actions on immigration and want to go to conference with the Senate to work out their differences .

Implications for Boehner

How he handles the showdown could dictate the rest of his speakership, as House conservatives warn compromising now means he's effectively allowing Democrats to block GOP agenda for the next two years.

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The Senate approved a longer-term funding bill Friday even though it wasn't expected to go anywhere in the House. On a 68-31 bipartisan vote, the Senate cleared a so-called "clean" DHS bill, after stripping of provisions opposed by Democrats that would have blocked Obama's immigration orders.

Even as he and Senate Majority Leader Mitch McConnell deployed completely different strategies to address the impending funding lapse, Boehner insisted the GOP is on the same page.

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"It is not a fight amongst Republicans. All Republicans agree we want to fund the Department of Homeland Security and we want to stop the President's executive action with regard to immigration," he said.

Court ruling

Some Senate Republicans are urging the House to point to the recent ruling by a Texas judge to suspend the administration's program to process visas for those wanting to remain in the country.

"The courts have acted. Accept the victor that the courts have given us, which is the President does not have the authority to do what he has done and vote to continue to fund the Department of Homeland Security. I think that is the right decision," Sen. John Barasso, R-Wyoming, said on CNN on Thursday.

Some conservatives have said they don't feel any pressure to fund the agency before the deadline because most employees would still be required to come to work. Rep. Tim Huelskamp, R-Kansas, told CNN that employees at the agency just got paid last week so there is enough time to debate the issue before they need to approve continued funding, even on a short term basis.

Homeland Security Secretary Jeh Johnson dismissed that notion and told reporters "that minimizes the impact of forcing people to work without a paycheck" and said he continues to press for "full funding."