Yet it remains unclear whether there is enough support among rank-and-file Republicans to pass such a measure, or whether House Democrats would agree to vote for it, rather than the bill the Senate is expected to pass later this week.
Some conservative members have vowed not to vote for any bill funding DHS that does not also block Obama's action. But even centrist Republicans may find such a short-term measure objectionable, either because it does not fund the agency for a long enough period of time, or out of fear of blowback from constituents and outside groups.
Meanwhile, House Minority Leader Nancy Pelosi said earlier in the day that her caucus is "not prepared to do a two-month CR," citing the uncertainty associated with short-term funding and highlighting programs that would be harmed without a full bill. And Reid said only that he wanted to avoid discussing hypotheticals.
But within the rank and file, members said they'd heard no messaging from leadership on whether they should support a CR. Most said they'd hold their decision until they saw a bill from GOP leadership, but Rep. Gerry Connolly—whose Northern Virginia district includes a huge number of federal workers—said he would resignedly back such a measure. "I'm somebody who has a fairly consistent record of doing everything I can to avoid shutdowns, partial or otherwise," he said. "So if my only choice is a clean, short-term funding bill, obviously I would support that."
Opposing a CR could be politically risky for Democrats after weeks spent warning of the national security dangers that would come with a DHS shutdown. One senior House Democratic aide said this week that any clean funding measure—short-term or otherwise—would be a cave on the part of Republicans, and one that Democrats should eagerly accept.
House Democratic Whip Steny Hoyer, however, said Thursday he will not help provide Democratic votes for a short-term CR and that Republican leaders have not asked him to. Instead, he called on House GOP leaders to pass the clean, full-year funding bill that the Senate looks to pass by the end of the week.
"I don't think so," a frustrated Hoyer said. "They continue to construct cul de sacs for themselves, running into cul de sacs, dead ends, then we play this game all over again."
Homeland Security Department Secretary Jeh Johnson was on Capitol Hill on Thursday, meeting with members and advocating for a full-year funding bill. He told reporters outside of the House chamber that a CR would not be enough.
"We need a fully funded Department of Homeland Security in these challenging times. "¦ We need a full-year appropriations bill for the department to fund all of our key missions," Johnson told reporters. "I'm optimistic, because I have to be on behalf of the men and women of my department, but I realize that this is going to take a lot of sustained effort to get where we need to be, which is why I'm up here."
This story has been updated.
Alex Brown contributed to this article