As the possibility of a government shutdown comes closer, House Speaker John A. Boehner (R-Ohio) has not yet asked House GOP freshmen if they would accept the kind of compromise Democrats say is on the table.

For days, Democrats have said they are close to an agreement that would cut about $33 billion from the federal government’s budget this year. Boehner has said there is no agreement on a number, although congressional aides have said privately that this offer remains.

Boehner has not asked members of a key Republican bloc if they would approve such a deal, his spokesman and lawmakers say.

“The Speaker says there’s no figure in mind at all, that that’s all been misquoted. Nobody knows of a $33 billion figure, except what we read in the paper,” said freshman Rep. Billy Long (R-Mo.).

“He’s been very clear on that, that there is no number. Never has he asked us” to give an opinion about the $33 billion figure, said Rep. James Lankford (R-Okla.), another freshman. “There has been no vote on that, no proposal from him on that.”

Michael Steel, a spokesman for Boehner, confirmed that the speaker has not specifically run the $33 billion figure by freshmen members.

“That’s not really the way that works,” Steel said. He said Boehner felt confident that he knew the freshmen’s wishes on this subject, and did not think it necessary to discuss specific offers and counter-offers with them.

“You don’t go back to 242 guys, and say, ‘Well, is $23 [billion] okay?’ ‘Nope.’ ‘Is $27 okay?’ ‘No,’” Steel said, referring to the 242 Republicans in the House. Freshmen account for 87 of them.

The $33 billion figure is only about half of the $61 billion that the House voted to cut earlier this spring. The Democrat-led Senate has not agreed to that. The impasse between the two parties, and the two congressional chambers, now threatens to shut down the federal government after Friday.

In the middle of all this is Boehner himself. He must either find a way to convince freshmen and conservative Republicans to accept some kind of compromise with Democrats or he must take the political risk of shutting down the government. Congressional rules dictate that some kind of compromise must be reached by Tuesday night, or there may not be enough time for a bill to pass all the procedural hurdles and be approved.

For now, Steel said, Boehner “hasn’t — and wouldn’t — agree to $33 billion in cuts. ... His job is to fight for the largest possible cut.” Steel said that Boehner knows Republicans’ wishes well enough already, from repeated meetings with them.

In an interview Tuesday, Rep. Jim Renacci (R-Ohio), another freshman, said he’s not aware of Boehner having asked whether his members would be willing to come down to $33 billion.

“The caucus has been pretty solidly unified on working toward the $61 billion cuts and we’re moving forward toward that,” he said. “We’re continuing to work toward that number.”