WASHINGTON -- House Republicans inched closer to embracing a stopgap measure to prevent a Department of Homeland Security shutdown on Thursday, a day before the agency runs out of money.

GOP leaders huddled with their conference behind closed doors to gauge support for a three-week continuing resolution that would keep DHS running, a day after the Senate intensified pressure on the lower chamber by preparing to vote on a "clean" DHS funding bill.

House members leaving the meeting expressed disappointment in Senate Republicans, who on Wednesday reached a deal with Democrats to advance a measure that would fund DHS absent any riders aimed at blocking President Barack Obama 's executive actions on immigration . Frustration was especially palpable among House conservatives, who refused to throw in the towel on using the power of the purse to curb Obama actions that would provide deportation relief and work permits to millions of undocumented immigrants.

"I would like to have seen more cloture votes taken and the Democrats who are actually the ones at the helm of forcing this impossible conundrum to be pointed out to the public in a better way," Rep. Trent Franks (R-Ariz.) said of the Senate, adding that he wasn't sure how he would vote on a short-term continuing resolution.

Several rank-and-file members who talked to reporters after the meeting cast doubt over whether House GOP leaders would have enough votes for their plan, which a leadership aide confirmed was to pass a short-term continuing resolution on Friday, as well as a motion to go to conference with the Senate. House Minority Leader Nancy Pelosi (D-Calif.) said earlier in the day that she told House Speaker John Boehner (R-Ohio) that Democrats were not interested in supporting a continuing resolution.

A House Democratic leadership aide said Democrats will be encouraged to vote against the short-term bill. "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," the aide said.

The House gambit to go to conference isn't likely to get a warm reception in the Senate, where at least some Democrats would need to agree to it. Senate Minority Leader Harry Reid (D-Nev.) said unequivocally earlier in the day that Democrats would not allow a conference, calling it "a waste of time."

House Republicans said they think that may change.

"Harry Reid isn't God. We'll see how he does," said Rep. John Carter (R-Texas), who chairs the House Homeland Security Appropriations Subcommittee. Carter said he would support a clean full-year bill or the short-term plan.

Part of the equation is a lawsuit against the president's executive action filed by 26 states, being considered by a federal judge in Texas. The judge issued a preliminary injunction last week that halted Obama's new executive action programs from moving forward as he considers their constitutionality. The Obama administration is seeking a stay of that decision that would allow the programs to begin, and is appealing.

The three-week continuing resolution may fund DHS until further rulings in the lawsuit, but it's more likely that the legal process will stretch out for months.

Still, Rep. Tom Cole (R-Okla.) said the sense among House Republicans was that the court was moving in their favor, so they were winning the broader fight against Obama's executive actions. A short-term continuing resolution and a House-Senate conference, he added, would buy Republicans more time to see how the issue plays out in the courts while putting the onus back on Democrats.

"I think a lot of them would feel pressure," Cole said. "It's not an unreasonable request. I think it'd be pretty hard for them once we guaranteed funding to say we don't want to sit down and talk about it at all."

Rep. Raul Labrador (R-Idaho) told reporters he thought the plan was a good idea, except it wasn't clear how Republican leaders planned to actually get the Senate to go to conference.

"Without the conference, we're just punting and passing the baton on to something else," Labrador said.

Not all Republicans supported the strategy, with some citing how it would look to risk a DHS shutdown amid high-profile terrorist threats, and others not seeing the point in stirring up the same fight in just three weeks.

Rep. Charlie Dent (R-Pa.) told reporters his message to his colleagues during the meeting was that "bad tactics yield bad outcomes."

"I think at this point we've engaged in an exercise of tactical malpractice, self-delusion and self-destruction," Dent said. "Some folks have a harder time to face the political reality than others. Some people want to be able to save face and get something from the Senate ... and I said we're not going to get anything."