WASHINGTON — The Senate is moving forward on legislation to fund the Homeland Security Department, but the House is in limbo two days away from a partial agency shutdown as conservatives angrily reject the Senate plan.

Many House Republicans say they aren’t ready to admit defeat and approve spending for the department without demanding concessions from President Barack Obama on immigration. They are pressuring House Speaker John Boehner to hold firm against that approach, even as Senate Majority Leader Mitch McConnell argues that it’s the best way out of the GOP’s dilemma.

No other options are apparent, aside from a partial shutdown of the agency charged with protecting the U.S. against terrorism. Without congressional action, that will happen at midnight Friday — and polls show Republicans likely to take the political blame.

Boehner met privately with McConnell on Wednesday afternoon, their first meeting in two weeks, but he gave no indication during the day of how he might resolve what has become a high-stakes leadership test two months into full Republican control of Congress.

“I’m waiting for the Senate to act. The House has done their job,” Boehner said at a news conference where he repeatedly sidestepped questions about his plans.

Hours after Boehner spoke, the Senate did act, voting 98-2 to advance the Homeland Security funding bill over its first procedural hurdle. Several more votes will be required to bring the bill to final passage, but that outcome in the Senate is assured with lawmakers of both parties ready to put the fight behind them.

The $40 billion legislation would fund the agency through Sept. 30.