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 would likely take the political blame.

Some conservatives have downplayed the implications of a partial shutdown, noting that of the department’s 230,000 employees, some 200,000 would continue to report to work because they are deemed essential, although they would not get paid until the situation is resolved.

Front-line employees at agencies such as Customs and Border Patrol, the Secret Service and the Transportation Security Administration would continue to report to work. Airport security checkpoints would remain staffed, immigration agents would be on the job, air marshals would do their work and Coast Guard patrols would sail on.

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, the end of the budget year. Gone would be the contentious immigration language from the House-passed version that repealed Obama executive actions as far back as 2012 granting work permits and deportation stays to millions of people in the country illegally, including immigrants brought here as kids.