House Republican leaders are privately warning Speaker John Boehner that they may not have the votes to pass a six-month spending bill with significantly less than $61 billion in cuts, and they are chafing at his closed-mouth style of negotiating.

Boehner, Senate Democrats and the White House are zeroing in on $33 billion in spending cuts. But the Ohio Republican is finding significant resistance from his top lieutenants, who have repeatedly warned they cannot sell that number to rank-and-file Members, insisting on at least $40 billion in cuts.

According to sources close to the issue, during a leadership meeting this week Majority Leader Eric Cantor (Va.), Majority Whip Kevin McCarthy (Calif.) and Republican Conference Chairman Jeb Hensarling (Texas) reiterated their concerns with Boehner’s handling of the talks. According to these sources, Boehner’s fellow leaders are concerned that a smaller deal will not muster the 218 Republican votes needed for passage. In fact, several sources said that at one point McCarthy bluntly warned they would lose a significant number of GOP votes if the deal is based on $33 billion in cuts.

Boehner spokesman Michael Steel downplayed the frustrations of the leadership team, chalking it up to general anxiety over the slow state of negotiations and a lack of action by the Senate.

“More than 40 days after the House passed a funding bill for the remainder of the year that cuts spending to help create jobs, I think everyone is frustrated that the Senate has failed to act,” Steel said.

“But our team is working together, focused on our shared goal: getting the biggest spending cuts possible enacted into law,” he added.

But others said that the frustration also stems from Boehner’s handling of the issue and that even if Boehner does deliver a deal above the $40 billion mark, that still might not be enough even for some in leadership.

“You’d have to find a bill close to $61 [billion], or at least in the high $50 [billions],” said Rep. Tim Scott, a freshman member of GOP leadership.

“My theory is that between now and next Friday there is going to be a deal cut. It’s not going to be $33 billion. It’s going to be significantly higher for us to be at the table, the freshman class specifically,” the South Carolina Republican said.

Republicans said Boehner’s fellow leaders are particularly concerned with the prospect of having to rely on Democratic votes to pass the bill, arguing that it will set a bad precedent for future difficult issues, most notably the looming debt limit vote.

“This is going to be nothing compared to the debt limit,” one GOP aide said.

Beyond concerns with the actual number that Boehner has been negotiating, Republicans said there is growing frustration with the lack of information that Boehner has provided to rank-and-file Members and to members of his leadership team.

For days, Boehner has walked a thin line in responding to questions from reporters about the tentative agreement on $33 billion in cuts, denying that there is a final deal while hinting that the agreement won’t include as many reductions as conservatives would like.

For instance, Boehner told reporters on Friday: “There is no number; there is no agreement on a number. We are going to fight for the largest spending cuts that we can get, and I’m hopeful that we’ll get it as soon as possible.”

Although strategically that sort of rhetoric makes sense for public consumption, aides said Boehner has been equally obtuse in discussing the talks with Members. During a meeting Thursday with freshmen, he repeated his argument that no final spending-cut amount is in place and will not be until agreements on all parts of the bill are reached.

Publicly, at least, rank-and-file Members deny there is frustration with GOP leaders for not sharing more details on the status of the negotiations and the specifics of a potential deal.

“I like leadership; I trust leadership,” Rep. Steven LaTourette said. While the Ohio Republican acknowledged that there have been no new details, he said that isn’t such a bad thing.

One GOP aide said Members are particularly frustrated given the fact that while Boehner may publicly insist no deal has been reached, others close to the talks are privately confirming the arrangement.

“There seem to be a number of aides ‘in the know’ confirming numbers that would be far less than ideal for a lot of House Republicans, and that confirmed-unconfirmed information is creating a sense of unease and confusion,” the aide said.

Even House leaders are being kept in the dark. While Boehner has regularly briefed his leadership team during negotiations to keep them up to date on the talks, GOP aides said he has largely kept his comments limited to his public statements.

Steel dismissed the notion that Boehner has withheld information from his colleagues. “Boehner is a pretty straightforward person.  What he’s telling members of our Conference — and the American people — is the same thing he is telling President Obama” and Senate Majority Leader Harry Reid (D-Nev.), Steel said Friday.

Nevertheless, the amount of information that Boehner’s lieutenants do have has led to some difficult moments for Cantor and others. For instance, during a meeting with reporters last week, Cantor came under pressure to discuss whether he would support a deal based on $33 billion in cuts.

During the tense exchange, Cantor initially pushed back, insisting no such deal was confirmed. But after being told that Republican and Democratic sources were confirming a $33 billion spending-cut total, a clearly frustrated Cantor simply said: “I have not been told by both sides that. So that is what I am saying. There is a difference in my knowledge base.”