House Speaker John Boehner of Ohio, right, and others, look on as House Majority Leader Eric Cantor of Va. speaks during a news conference on Capitol Hill Wednesday. (Harry Hamburg/AP)

If approved by the House and Senate, the stopgap funding bill -- which is the seventh such short-term measure this year -- would buy congressional leaders and the White House a few more days to work out a longer-term funding agreement through the end of the fiscal year in September.

It would also fund the Defense Department through the duration of that period, a response to calls from the Pentagon as well as key lawmakers such as Senate Minority Leader Mitch McConnell (R-Ky.) and Sen. John McCain (R-Ariz.) not to leave defense funding in the lurch as the budget stalemate continues. Already, this fiscal year marks the longest period that the federal government has gone without an agreed-upon budget since at least the late 1970s.

And the one-week measure would include a provision that would prevent federal and local funds from going toward providing abortions in the District of Columbia – a nod to social conservatives who have pushed for the inclusion of policy riders in any final funding agreement.

“We hope the White House and Senate Democrats will get serious about making real spending cuts on a long-term bill, but this measure provides us with an option if House Republicans choose to use it,” House Speaker John Boehner’s (R-Ohio) office said in a statement after a closed-door caucus meeting Monday night.

In recent weeks, rank-and-file members of both parties have expressed increasing dissatisfaction with the idea of passing a seventh stopgap measure, although leadership had not expressly ruled out the possibility.

Democrats had yet to weigh in on the proposal Monday night, but several Republican House members said in interviews after the closed-door meeting they would be open to backing a short-term bill if it either provided for longer-term defense appropriations or made significant progress toward achieving the $61 billion in cuts House Republicans proposed in their budget measure, H.R. 1, which was rejected by the Senate.

“I’m looking at the goal of achieving as much of H.R. 1 as I can, period,” House Republican Conference Chairman Jeb Hensarling (Texas) said. “Now, if I can achieve that in one bill, I would like to do it. If I can achieve it in two bills, I’d like to do it. If it takes fifty bills, so be it, but the goal is how much of H.R. 1 can we get passed so that we can create jobs, quit borrowing 42 cents on the dollar, much of it from the Chinese, and sending the bill to our children and grandchildren.”

Utah Republican Rep. Jason Chaffetz said he would likely approve another stopgap, “as long as we’re moving in the right trajectory.”

“If we have to come back and do this every week, so be it,” Chaffetz said. “I don’t have a problem with that. If that’s what it’s going to take, then let’s vote on it every day if we have to.”

New Jersey Republican Rep. Scott Garrett, vice-chairman of the House Budget Committee, said defense funding would likely have to be included in any new stopgap measure, but he declined to say whether he believed there was appetite among House Republicans to back a seventh short-term measure.

“That is the $64,000 question,” Garrett said.

While the introduction of the new short-term measure provides a safety net of sorts in case the parties fail to reach a longer-term agreement this week, Boehner also told Republicans Monday night that he has instructed Rep. Dan Lungren (R-Calif.), the chairman of the committee on House Administration, to issue guidance to all members on how to go about preparing for a potential government shutdown.

Boehner, Senate Majority Leader Harry Reid (D-Nev.), House Appropriations Chairman Hal Rogers (R-Ky.) and Senate Appropriations Chairman Daniel Inouye (D-Hawaii) are expected to meet with President Obama at the White House later Tuesday to discuss the way forward on funding the government.

Click here to see the full outline from House Appropriations Chair Hal Rogers’ (R-Ky.) office on what the latest one-week stopgap measure would entail.