For the second time in two weeks, congressional leaders engaged Monday in a battle via press release over ongoing federal budget negotiations as a government shutdown deadline loomed.

The first jab came shortly after 3 p.m., when House Speaker John Boehner (R-Ohio), who is facing pressure from his right flank to win deep cuts, said that the parties are far from agreement on a number to cut from the federal budget. He also criticized as inadequate the $33 billion that Democrats and the White House have said was agreed to.

“As I’ve said for a week, there is no agreement, and will be no agreement on a number until everything – including the important policy provisions from H.R. 1 – is resolved,” Boehner said in his lengthiest statement in recent days. “Despite attempts by Democrats to lock in a number among themselves, I’ve made clear that their $33 billion is not enough and many of the cuts that the White House and Senate Democrats are talking about are full of smoke and mirrors. That’s unacceptable.”

House Majority Leader Eric Cantor (R-Va.) and Majority Whip Kevin McCarthy (R-Calif.) issued statements within a half-hour after Boehner’s, emphasizing that if the government shuts down Friday, it will be Democrats’ fault.

“If the Democrats demand to defend every dime of government spending and force a government shutdown, that will be on their hands,” Cantor said, accusing Democratic leaders of “promoting false promises and using sleight-of-hand budgeting to achieve an imaginary spending-cut figure that is still far too low by comparison.”

That brought rejoinders from the offices of Senate Majority Leader Harry Reid (D-Nev.) and Sen. Charles Schumer (N.Y.), the third-ranking Democrat, which cast Republican leaders as divided between their desire to agree to $33 billion in cuts – the leaders’ original proposal – and the desire of their party’s conservative members to cut $61 billion.

“As we get closer to a final agreement, we are confident that in the end Republicans will reject cries from the tea party to shut down the government and work with us on a solution that makes smart cuts while protecting our economy’s recent gains,” Reid spokesman Jon Summers said in a statement.

Schumer’s statement was the final one – thus far – of the day, and it included a new twist on Democrats’ message: While House Republicans have disputed that any tentative agreement has been reached, Schumer argued that talks are so far along that anything short of a bipartisan agreement would amount to a turnaround by Boehner.

“This is an historic level of spending cuts, it is the halfway mark between the two sides, and the speaker has already agreed to this number privately. ... At this point, we are so far down the road towards an agreement, and so little time remains before Friday’s deadline, that it would be a dramatic about-face for the speaker to suddenly let things devolve into a shutdown, as many in the Tea Party are urging,” Schumer said.

The public posturing could be obscuring the fact that progress is being made behind the scenes – or it could be a sign that the negotiations aren’t going as well as hoped.

More should become clearer Tuesday, after House Republicans and Democrats hold weekly closed-door caucus meetings and the parties in the Senate hold their weekly luncheons. House Republicans are also holding a closed-door meeting Monday night to discuss budget issues.

Later Tuesday, Boehner, Reid, Senate Appropriations Chairman Daniel Inouye (D-Hawaii) and House Appropriations Chairman Hal Rogers (R-Ky.) are slated to meet at the White House with President Obama.