Updated: 1:45PM EST
A closed-door meeting on Tuesday between President Obama and a select group of congressional leaders failed to yield a compromise on a 2011 budget agreement, House Speaker John Boehner said in a statement after the meeting.
A spokesperson for Boehner said on Tuesday morning that "while there was a good discussion, no agreement was reached" during the meeting" - and that House Republicans were now rallying behind a possible third option: a Continuing Resolution that would keep the government running for another week while cutting an additional $12 billion in spending.
The White House isfor a bill that would fund the government after the current stopgap spending measure expires on April 8. But Republican and Democratic congressional leaders alike have demonstrated in recent days that they will go only so far in compromising their positions on the remaining issues.
Mr. Obama on Monday invited Boehner, Senate Majority Leader Harry Reid, Senate Appropriations Chairman Dan Inouye and House Appropriations Chairman Hal Rogers to participate in negotiations over the measure.
According to Boehner's statement, released by his staff after the meeting, the Ohio Republican said he told Mr. Obama "the House will not be put in a box and forced to choose between two options that are bad for the country."
He also disputed White House statements that the two parties had agreed on $33 billion worth of cuts in the budget.
"There has never been an agreement on $33 billion as an acceptable level of spending cuts, and that $33 billion in cuts is not enough, particularly when it is achieved in large part through budget gimmicks," Boehner said.
Rep. Steny Hoyer, the House's number two Democrat, said on Tuesday he would oppose another stopgap spending measure - and encouraged other House Democrats to follow suit.
"I will oppose this bill. ... I hope other Democrats will oppose it. I don't know that every Democrat will oppose it; There will be some things in there that they perhaps think are appropriate," Hoyer told reporters on Tuesday, according to the Washington Post.
Rep. Eric Cantor said on Tuesday that the White House had also dismissed the notion of another stopgap measure, and accused the Obama administration of "raising the risk of a government shutdown."
In remarks before the budget meeting this morning, however, White House Press Secretary Jay Carney declined to comment on Cantor's assertion.
"It is not necessary to continue a process of short-term [CRs] when an agreement is within reach," he said, according to the Hill.
Inouye said after the meeting he thought a government shutdown could be averted because "we are people of good faith."
Republicans on Monday night introduced a proposal for a stopgap measure that would continue to fund the federal government for a week, would fund the Defense Department through September, and which calls for an additional $12 billion in cuts across federal agencies.
The measure would also prohibit Washington, D.C. from spending its own money to provide abortions for low-income women, according to the Washington Post.
In a statement on Tuesday, D.C. Delegate Eleanor Holmes-Norton (D) said the new bill demonstrated Republicans' "contempt" for the residents of the District of Columbia.
"With this one-week CR, Republicans have demonstrated their contempt for the American citizens who reside in the District of Columbia," Holmes Norton said, the Washington Post reports. "The only other prohibition in the bill would prevent Guantanamo Bay detainees from being brought into the United States. District residents are not easy bargaining chips to be used like non-citizens at Guantanamo Bay. We are not surprised by this insult from House Republicans. We will be outraged if President Obama, Majority Leader Reid and the Senate Democratic majority throw the District of Columbia under the bus because of how the city chooses to spend its own local funds."