A federal judge left Congress in a tougher spot Tuesday with his order to temporarily halt the Obama administration's implementation of a new immigration policies, heightening tension as a Feb. 27 deadline looms for funding the Department of Homeland Security.

Officially, House Speaker John A. Boehner (R-Ohio) and Senate Majority Leader Mitch McConnell (R-Ky.) said the ruling backed up their belief that President Obama's actions were unconstitutional, and that Senate Democrats should stop filibustering a funding bill that includes repeals of the presidential orders protecting up to 5 million illegal immigrants from deportation.

Behind the scenes, both sides were trying to determine what impact the ruling would have on an already charged legislative atmosphere on Capitol Hill. Some said Republican leaders would now be able to point to the court case as the strongest venue for taking the fight on Obama's immigration orders -- potentially allowing for approval of overall funding for DHS without the policy riders restricting the president.

Others viewed the ruling as more likely to encourage the far-right flank of Republicans to dig in for a fight and let funding for the department lapse rather than cede any ground on an issue they call "executive amnesty."

Congress is out of session this week and does not return until Monday night. That will leave just four full days to reach a pact or see the partial shutdown of an agency tasked with protecting borders and airlines, responding to natural disasters, and helping assess domestic terror threats.

"He doesn’t have the authority to take the kinds of actions he once referred to as 'ignoring the law' and 'unwise and unfair.' Senate Democrats -- especially those who've voiced opposition to the President’s executive overreach — should end their partisan filibuster of Department of Homeland Security funding," McConnell said in a statement

"We will continue to foll the case as it moves through the legal process," Boehner said in his statement. "Hopefully, Senate Democrats who claim to oppose this executive overreach will now let the Senate begin debate on a bill to fund the Homeland Security department."

Conservative activists, along with allies such as Sen. Jeff Sessions (R-Ala.), have pushed Boehner and McConnell to be willing to shut down DHS over the immigration issue, saying that Democrats will be blamed and Obama will eventually relent. Other Republicans fear a repeat of the October 2013 shutdown of the entire federal government, when the public disproportionately blamed the GOP Congress for the standoff.

Many party elder statesmen have warned that a shutdown of the agency designed to protect against domestic attack would be particularly dangerous from a political perspective.

"I think it would be terrible. The American people didn't give us the majority to have a fight between House and Senate Republicans. They want things done," Sen. John McCain (R-Ariz.) said Sunday on NBC's "Meet the Press". "We cannot cut funding for the Department of Homeland Security. We need to sit down and work this thing out. And there's ways we can address what the president did was unconstitutional. But it's not through shutting down the Department of Homeland Security. It's too serious."

Most security workers would be deemed essential in a DHS shutdown and report to the border or to airports, but they would go without pay, while tens of thousands of administrative-level workers would be furloughed.