Congress is now in a full-fledged stalemate over a bill stuck in the Senate to fund the Department of Homeland Security and roll back President Obama’s executive actions on immigration, now that House Republican leaders have declined to help.

Top House Republicans stated their position after Senate Majority Leader Mitch McConnell suggested they draft and pass a new bill, which they could send to the upper chamber and that Senate Democrats would accept.

“We did our work to make sure the Department of Homeland Security is fully funded while also defying the president’s unconstitutional executive action on immigration,” House Majority Leader Kevin McCarthy said Friday.

The California Republican’s remarks were part of a memo to fellow House members recapping the first six weeks of the 114th session. They followed similar remarks a day earlier by House Speaker John Boehner.

"The House has done its job,” the Ohio Republican said. “And now it's up to the Senate to do their job."

Boehner and other congressional Republicans are blaming Senate Democrats for filibustering attempts to even debate the bill in the upper chamber.

Funding for the agency expires Feb. 27. And Congress in out of session until Feb. 24, which means members will have just four days to strike a deal before the agency loses much of its funding.

McCarthy further suggested the lower chamber has no plans to revisit the issue when he wrote in the memo: "When we return at the end of this month, the House will start quickly with a series of bills expanding equal opportunity in education."

The standoff and the party’s efforts to blame each other is a setback for Republicans who had hoped that winning the Senate in November to take full control of Congress this year would end at least some of the bipartisan gridlock that has frustrated Americans.

"I suppose elections have consequences, except in the United States Senate," complained GOP Rep. Mick Mulvaney of South Carolina. "Tell me how it would be different” if Nevada Democratic Sen. Harry Reid was still the Senate majority leader.

Though Republicans control the upper chamber, they are six votes short of the 60 needed to advance most legislation, and Senate rules grant numerous rights to the minority party. That means if Democrats remain united, they have the ability to block GOP bills just as they did while in the majority.

Republicans now have a few choices on the DHS-immigration bill -- pass a short-term extension of current funding levels, strip the bill of the immigration language opposed by Democrats, or let the agency run out of money.

Though all of those options appear unfavorable to Republicans, some House conservatives argue a shutdown would hardly be calamitous because the large majority of department personnel would be deemed essential and report to work, though most would not get paid until after the shutdown ends.

"Look at the last shutdown -- 85 to 90 percent of the personnel from DHS all came to work, and they all got paid" eventually, said Rep. Matt Salmon, R-Ariz. "As much as both sides don't want that to happen, it is always a possibility."

The last shutdown happened in the fall of 2013 over a failed GOP attempt to uproot Obama's health care law. Republicans got blamed for that one, and some fear they would pay the political price if there's another one, too.

GOP leaders have announced that the Senate will resume by taking its fourth procedural vote on the House-passed funding bill.

But Democrats have blocked all three previous attempts to open debate on the measure. So the outcome is unlikely to be different the fourth time.

Meanwhile, the Obama administration is moving forward unchecked in implementing the new immigration programs, as a result of at least one executive action.

On Wednesday, U.S. Citizenship and Immigration Services will start accepting applications from those eligible for an expanded program granting work permits and deportation deferrals to immigrants brought illegally to the U.S. as children.

The Associated Press contributed to this report.