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 Gone would be the contentious immigration language from the House-passed version that repealed Obama executive actions as far back as 2012 granting work permits and deportation stays to millions of people in the country illegally, including immigrants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

Instead, McConnell envisions a separate vote on a narrower immigration measure to undo just Obama's most recent immigration directives, from November. The measure would leave in place protections enacted in 2012 for younger immigrants, but even so Democrats are not likely to approve that bill, and it faces a certain Obama veto.

The president repeated that threat Wednesday at a town hall style meeting in Miami designed to keep pressure on Republicans.

"If Mr. McConnell, the leader of the Senate, and the speaker of the House, John Boehner want to have a vote on whether what I'm doing is legal or not, they can have that vote," the president said. "I will veto that vote - because I'm absolutely confident that what we're doing is the right thing to do."

Facing united opposition from Democrats who blocked four GOP attempts to open debate on the House-passed bill, McConnell said he was offering the best plan he could. But House conservatives called it a surrender and said they would not abandon their fight, even if no outcome looked possible except a partial Homeland Security shutdown that would furlough 30,000 workers and send tens of thousands more to work without pay.

"On one side, we're faced with dealing with the horrible prospect of a shutdown. If we do nothing and we just capitulate, we're dealing with an even more horrible prospect of a constitutional crisis," said Rep. Matt Salmon, R-Ariz. "It's a no-win situation."

A number of Republican lawmakers said the plan could potentially pass with Democratic votes, but conservatives warned that Boehner would face an intense backlash if he took that route, as he's done in the past.

Congress could potentially pass a short-term extension of current funding levels, but that would only postpone the conflict.

House lawmakers openly chafed at the position they found themselves in after agreeing last fall to put off the fight over immigration until this year. The argument was that they would have more leverage once Republicans controlled the Senate and claimed larger numbers in the House.

That hasn't proven to be the case, mainly because the GOP commands only 54 votes in the Senate, short of the 60 needed to advance most legislation under the chamber's rules. And Obama's veto pen still gives him the ultimate leverage.