House Republicans on Thursday presented a plan for a stopgap bill that would fund the Department of Homeland Security for three weeks, raising hopes of averting a looming shutdown of the agency.

The plan, which the leaders pitched to rank-and-file Republicans in a closed-door meeting, was the first sign they were willing to pass a new bill after passing another one weeks ago that takes aim at President Obama’s executive actions on immigration and has been blocked in the Senate. But the plan faces an uncertain outlook, as House Democratic leadership decided to marshal support against it.

Facing a Friday-night-into-Saturday-morning shutdown deadline, the plan might ultimately win support from lawmakers in both parties on Friday. But its passage would only continue a standoff between the House and the Senate over longer-term DHS funding. Separately, the Senate was moving toward a final vote on a funding bill that would not go after Obama’s immigration directives.

Exiting the House GOP meeting, Republican members said the leadership presented the plan as a way to allow time for the House and Senate to try to go to conference on their competing bills. But Senate Democratic leaders have rejected the idea of a conference.

Rep. Walter B. Jones (R-N.C.), a foe of House Speaker John A. Boehner (R-Ohio), said that he would not support the plan but that of those who spoke, a “majority, probably, are inclined to support it.”

Rep. Richard B. Nugent (R-Fla.), who has also clashed with Boehner, said he would support the proposal.

“I think the speaker has laid out a plan. Obviously, he can’t control what the Senate does,” Nugent said.

The GOP meeting came as the Senate’s bill appeared unlikely to face tactical delays from rogue conservative senators who want to battle Obama. The measure could win final passage Friday.

One of the leading critics of the president’s immigration actions, Sen. Jeff Sessions (R-Ala.), said he did not plan to hold up the measure and was “not aware” of others planning to do so.

“I think it’s appropriate to move forward with the bill,” Sessions said. “Ideas about how the process will go forward seem to be firming up. I’m not happy with them, but I’m not interested in delay merely for the sake of delay.”

But House Republican leaders, bent on fighting Obama’s directives, did not embrace the Senate plan.

Boehner declined to say whether he would take the Senate bill up in his chamber. He said Thursday morning that the House has done its part by passing its own bill.

“We’ll wait to see what the Senate can or can’t do,” Boehner told reporters. He accused Senate Democrats of “blackmail to protect the actions of the president.”

Meanwhile, Democrats ramped up pressure on Boehner to take up the measure. Speaking at a joint news conference, Senate Minority Leader Harry M. Reid (D-Nev.) and House Minority Leader Nancy Pelosi (D-Calif.) called on Boehner to swiftly bring it to a vote and warned Boehner not to amend it with immigration riders.

“It is a waste of time. We will not allow a conference to take place,” said Reid, addressing the possibility of a House-Senate conference.

The Senate bill, which Majority Leader Mitch McConnell (R-Ky.) put forward after it became clear the House bill would not advance in his chamber, already cleared a key procedural hurdle. It remained possible the Senate could vote on it Friday.

Reid declined to say whether he would try to block a short-term stopgap bill if the House passed one. Pelosi argued that a short-term bill is not an ideal solution.

“It’s harmful to our national security, our homeland security, for us to be inching along, whether it’s two months, four months,” she said.

Congressional Democratic aides sent conflicting signals Thursday evening. Some suggested their leadership would probably supply enough votes for the bill while others said they would try to defeat it.

“If House Republicans want to end up with another manufactured crisis that risks our national security in a matter of days, they can do it with 218 votes of their own,” said a House Democratic leadership aide, who spoke on the condition of anonymity to discuss strategy.

Democrats pointed to dangers the United States is confronting as the DHS debate is unfolding. They cited the threat of the Islamic State, the mass shooting at a French satirical newspaper and concerns about disaster preparedness.

And Democrats lambasted the Republicans for not moving more quickly.

“I have a grandson in eighth grade, and his knowledge about how to pass a bill is superior to what we’ve seen among the Republicans,” Pelosi said.

At least one member said he would forgo pay during a DHS shutdown, in solidarity with nonessential employees facing the prospect of a furlough.

“As long as the employees of the Department of Homeland Security including Border Patrol, Coast Guard and TSA are working while not receiving paychecks, I will ask that my paycheck be withheld,” Rep. Brad Sherman (D-Calif.) said in a statement.

Rep. Tim Huelskamp (R-Kan.), a conservative critic of GOP leadership, said Boehner is handling the DHS fight “as best as can be expected.” But in a sign of lingering House-Senate tension, Huelskamp lashed out at McConnell.

“Harry Reid’s still in charge. There are going to be millions of folks that helped change the Senate from Democrat to Republican [who] are going to be disappointed in Senator McConnell,” he said.

Mike DeBonis and Paul Kane contributed to this report.