WASHINGTON (AP) — In the heady days after winning control of both congressional chambers, Republican leaders vowed to keep the government funded and to block President Barack Obama from overhauling immigration policies on his own.

But House Speaker John Boehner and Senate Majority Leader Mitch McConnell never crafted a legislative strategy to accomplish those goals. And as events turned against them this week, McConnell said he didn't know how Boehner would handle a political dilemma heading his way. Boehner, in turn, acknowledged that he and McConnell haven't talked in two weeks, although their staffs often confer.

For all their victories in the midterm elections, Republicans have been loath to accept the limits of their success. Even with 54 of the Senate's 100 seats, they still lack enough votes to overcome filibusters, the bill-killing tactic that Democrats are now using against Republicans after years of being on the receiving end.

Senate Republicans confronted that cold reality Tuesday. McConnell publicly conceded he can't force Senate Democrats to allow action on a contentious House-passed bill. The bill would fund the Department of Homeland Security while also blocking Obama's 2014 executive order to protect millions of immigrants from deportation even though they are here illegally.

Senate Democrats insist the two issues be separated. McConnell reluctantly yielded Tuesday, and prepared to send House Republicans an unpleasant choice.

They can keep Homeland Security funded beyond this week, inviting fury from anti-Obama groups who want to use the funding as leverage on deportation policies. Or they can let the funding lapse, and invite the type of criticism they received for a partial government shutdown in 2013.

"To me, this is a test of the new majority," said GOP Sen. Lindsey Graham of South Carolina. Yet he, like McConnell, said he didn't know how the House would resolve the problem.

"I think Mitch's proposal is about as good as we'll get," Graham said. "We're not going to get the defunding bill through here," he said, thanks to Senate Democrats' solidarity.

After House Republicans huddled Wednesday, they showed no signs of budging. "We're waiting for the Senate to act," Boehner told reporters.

Many House conservatives refuse to acknowledge the Senate math that requires 60 votes to move almost any measure, senior Republicans say. Groups that prize ideological consistency over pragmatism continue to call on GOP lawmakers to refuse to fund Homeland Security unless Obama yields on deportation policies.

Michael A. Needham, head of Heritage Action, said spending bills are Congress' only tools "to rein in executive overreach."

Boehner, from Ohio, and McConnell, from Kentucky, are two of Congress' savviest and most experienced negotiators. Over the decades they've cut deals with Democrats on education, taxes and other issues. They have a cordial, if not chummy, relationship.

But a House speaker and a Senate majority leader must tend relentlessly to their colleagues' needs and grievances. It's an often thankless task that limits their ability to strike bargains with each other, let alone with presidents.

House members, in particular, have become increasingly partisan and ideological in recent years. That makes it ever more difficult for Republican and Democratic leaders to strike bipartisan accords.

GOP Rep. Matt Salmon of Arizona said Boehner would find himself "on very thin ice" as leader of the Republicans if he tried to pass a Homeland Security funding bill with mostly Democratic votes.

McConnell defended his strategy Wednesday. "The dual-pronged approach I've outlined — allowing the Senate to stop 'unwise and unfair' overreach on the one hand, and to fund DHS through the fiscal year on the other — is a sensible way forward," he said on the Senate floor.

The impasse also highlights the gap between the Republican Party's congressional wing and its presidential wing. Many GOP lawmakers — especially those from staunchly conservative House districts — say it's almost always politically safe for them to oppose Obama, illegal immigration and government bureaucracies.

To fund Homeland Security without clipping Obama's wings on immigration "is problematic back home," said Rep. Mark Meadows of North Carolina. Even if critics accuse Republicans of weakening Homeland Security at a time of terrorist threats, he said, a funding bill that fails to block "lawless actions on behalf of our president is not something we can stand."

Such rhetoric, however, may not play as well with important independent and Hispanic voters in presidential elections.

Graham, who is weighing a 2016 presidential bid, said he dislikes the Democrats' tactics, "but we'll get the disproportionate blame" if Homeland Security partly shuts down. As an advocate of tougher military action against terrorists, he said, "I can't have my fingerprints" on that.