WASHINGTON (AP) — A month into their newfound control of both chambers of Congress, it wasn't supposed to be like this for Republicans. Instead of advancing a conservative agenda and showing voters they can govern, they are confronting the very real possibility of a shutdown of the Homeland Security Department later this month.

That's because they can't 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 Barack Obama'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.

"If funding for Homeland Security lapses, Washington Democrats are gonna bear the responsibility," the Ohio Republican said. "Senate Democrats should stop blocking debate on the House-passed bill."

Some House conservatives go farther, arguing that 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."

Another lesson from the last shutdown, which happened in the fall of 2013 in a failed attempt to unwind Obama's health care law: Republicans get blamed. Even while insisting Senate Democrats are the ones courting a shutdown, many Republicans acknowledge they may have a hard time selling that idea to the public given that they control both chambers of Congress.

The predicament is so frustrating to House Republicans that some conservatives have begun advocating changing Senate rules to limit the use of the filibuster, an idea several Senate Republicans have already dismissed. For many, the fear is that their deadlock over the Homeland Security bill is merely a taste of things to come for the next two years.

Although Republicans were successful in clearing a bill authorizing the Keystone XL oil pipeline, setting up an Obama veto, many say that was a relatively easy lift that could stand as the exception rather than the rule in the months of divided government to come.

"Now we have the Senate and so our constituents think 'now you can stop Obama'. Well we don't have 60," said Rep. Tom Rooney, R-Fla. "Honestly it's going to continue to frustrate not only our side but the people who elected us that nothing is going to change until we get a new president."