WASHINGTON — It wasn’t supposed to be like this for Republicans. A month into their control of both chambers of Congress, they are confronting the very real possibility of a shutdown of the Homeland Security Department later this month.

Instead of advancing a conservative agenda and showing voters they can govern, the GOP has been unable to overcome Senate Democrats’ stalling tactics in a dispute over immigration.

“I suppose elections have consequences except in the United States Senate,” complained GOP Rep. Mick Mulvaney of South Carolina, summing up the frustration for many House Republicans. “Tell me how it would be different if Harry Reid were still running the place,” he added, naming the Senate Democratic leader who was booted into the minority in November’s midterm elections.

Although their party is now setting the floor schedule and calling hearings, Republicans are finding to their chagrin that important things haven’t changed from when they were in the Senate minority.

Republicans 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.

Democrats have been united against House-passed legislation funding the Homeland Security Department through September, the end of the budget year, while also rolling back President BarackObama’s executive policies on immigration.

As a result Congress appears to be at a stalemate on the issue, leaving Republicans with only a few options: pass a short-term extension of current funding levels, fold and strip the immigration language opposed by Democrats from the bill, or let the Homeland Security Department run out of money when current funding expires Feb. 27.

They’re all bad options from the GOP perspective. A short-term extension just pushes the problem to a later date. Removing the immigration language would amount to a bitter admission of defeat after Republicans have spent months accusing Obama of an unconstitutional power grab for limiting deportations for millions in the U.S. illegally. That’s left Republicans staring down the third possibility: a shutdown of the Homeland Security Department.

It’s something most say they want to avoid, but on Thursday House Speaker John Boehner refused to rule the possibility out, insisting instead that Senate Democrats should get the blame if it happens.