Congressional leaders worked late into the night on Tuesday to resolve last-minute issues with the bipartisan budget agreement reached between Congressional leaders and the White House, paving the way for the House to vote as early as Wednesday on the legislation.

The deal hit a snag Tuesday night after many Republicans raised questions about whether the $80 billion in spending increases in the legislation would be fully offset by spending cuts and other revenue. Conservatives continued to fight the bill throughout the night, including attempting to kill the bill in a late-night hearing of the House Rules Committee. But Republican leaders worked out last-minute fixes and the committee voted to clear the bill, setting up a possible Wednesday floor vote.

Some Republicans raised concerns that the bill only includes about $75.7 billion in spending cuts, according to the Congressional Budget Office, about $4 billion short of the $80 billion in spending increases.

Congressional leaders amended the deal late Tuesday to resolve the discrepancy. Boehner spokeswoman Emily Schillinger said the amendment included a “technical fix” to off-budget money, known as the Overseas Contingency Operations fund, that was used to help offset some spending.

“With this amendment, all budget cap relief is fully offset with mandatory spending cuts and other savings,” Schillinger said.

But the amendment did not resolve additional concerns about the deal and it is unclear how much support there will be for the deal among Republicans. Conservative members testified before the committee that they were angry with both the substance of the agreement and fact that it was negotiated in secret by outgoing House Speaker John Boehner (R-Ohio), who is expected to step down later this week.

What would be cut and what would be kept in outgoing House Speaker John Boehner's plan to raise the debt ceiling (Sarah Parnass/The Washington Post)

“It don’t feel right to me that we let the guy that’s leaving office do a budget that the rest of us have to live with, and we don’t even know where the new guy coming in stands on it,” said Rep. Curt Clawson (R-Fla.) during the late-night Rules meeting.

Boehner’s likely successor, Paul Ryan (R-Wis.), is said to have not been involved in the negotiations. In fact, Ryan strongly condemned the way the deal was assembled, explaining that he had yet to actually lay eyes on it.

“About the process, I can say this: I think the process stinks,” Ryan said.

Ryan added that “under new management,” the “people’s business” would be conducted differently.

Leaders were forced to combat a long list of sticking points on Tuesday, including anger from members who opposed a reduction in crop insurance payments, which would raise $3 billion over 10 years. The top members of the House and Senate agriculture committees released a statement on Tuesday opposing it.

“Make no mistake, this is not about saving money. It is about eliminating Federal Crop Insurance,” said House Agriculture Committee Chairman K. Michael Conaway  (R-Tex.). “The House Agriculture Committee was not consulted regarding any changes to policies under the jurisdiction of our committee.”

Others were upset that Boehner negotiated the deal in secret with the White House, House Minority Leader Nancy Pelosi (D-Calif.), Senate Majority Leader Mitch McConnell (R-Ky.) and Senate Minority Leader Harry Reid (D-Nev.). The small group kept a tight lid on the negotiations, revealing the deal only once it was complete.

Earlier in the day, Boehner conceded the deal was crafted before his departure because he didn’t want the new speaker “to walk into a dirty barn full of you know what.” He agreed that the package should have been assembled in a more inclusive way, saying, “This is not the way to run a railroad.”

Boehner presented the budget deal to his Republican colleagues at a private meeting Tuesday morning, outlining his plan to avert another government shutdown and raise the debt ceiling as a parting gift to his successor.

The deal would increase federal spending by $80 billion over two years and raise the federal borrowing limit through 2017. The 144-page bill, which was released Monday shortly before midnight, was welcomed by Democrats who have been pushing for budget negotiations all year.

“We have a budget agreement,” Boehner (R-Ohio) said after the meeting of House Republicans.

Boehner, who will step down on Friday, added that the alternative was a clean debt-ceiling suspension with no extra funding for troops. “This is a good deal,” he said.

Democrats largely embraced the plan. Vice President Biden praised the deal Tuesday.

“The last seven years, we’ve gone from crisis to recovery, and we’re on the verge of being able to have a genuine economic resurgence here,” Biden said. “And what we’ve put together is a good deal. No one got everything they wanted. But it will last for two years and it will prevent us from lurching from crisis to crisis.”

McConnell told reporters on Tuesday that the agreement reaches the issues that were important to Republicans, including more money for defense programs and offsetting funding increases through spending cuts rather than tax increases.

“I’m hopeful and optimistic that that bill will come over to the Senate, and when it does, we’ll take it up,” McConnell said.

Early indications are that key Senate Republicans are also on-board.

Senate Armed Services Committee Chairman John McCain (R-Ariz.) said he will support the budget deal because “it restores all but $5 billion of the defense requirements.” He said that if the budget agreement passes he could move quickly to adjust and pass the National Defense Authorization Act that was recently vetoed by President Obama over budget concerns.

McCain’s backing all but ensures the support of other defense hawks, including Sen. Lindsay Graham (R-S.C.), a GOP presidential candidate.

“We’re in a box here,” Graham said. “But if Senator McCain is okay with it, then I’ll probably be okay with it.”

Following the meeting Tuesday morning,  some conservatives complained that the negotiations were conducted without the input of committee chairs and rank-and-file members. But they’re unlikely to have the numbers to derail the pact as long as Democrats and moderate Republicans stay onboard.

“I don’t know if this thing could pass,” said Rep. John Fleming (R-La.), a member of the House Freedom Caucus. “It could break apart, and we could begin tackling this piecemeal well into Paul Ryan’s speakership.”

Centrists such as Rep. Tom Cole (R-Okla.) said that the deal isn’t perfect but that it prevents default and gives certainty to the military while making long-term reforms to Social Security and Medicare.

“I think it’s a pretty easy choice to make,” Cole said. “It’s a compromise and that means we had to give some things up that we don’t want, but we got some great things.”

Pelosi embraced the agreement Tuesday morning, signaling that the 188 House Democrats could provide a large portion of the vote needed to get a majority in the House.

“The bipartisan budget package unveiled last night represents real progress for hard-working families across the country,” Pelosi said. “I look forward to working toward House passage of this proposal this week. Next, we must move forward to complete the appropriations for FY2016 and keep government open.”

If Pelosi and House Minority Whip Steny H. Hoyer (D-Md.) can deliver votes from most, if not all, of their members, Boehner will have to win the support of only about 40 to 50 Republicans to pass the deal.

It would also take the pressure off Ryan. Conservatives will be closely watching whether Ryan supports the deal.

“I hope Paul Ryan will let us know how he feels about the process,” Rep. Justin Amash (R-Mich.) said Monday after a closed-door meeting of House Republicans.

White House officials also weighed in to back the proposal.

The agreement reached by congressional leaders last night meets these key tests: It provides substantial relief from harmful spending cuts, and it does so equally on the defense and non-defense sides of the budget,” one White House official said in an e-mail. 

The deal isn’t a complete victory for Democrats, who were pushing for even more spending increases and hoped to pass an increase in the federal borrowing limit without including it in a broader budget deal. Obama has insisted that the debt limit not be used as a negotiating tool for spending cuts. The deal allows Obama to say he secured a bargain on a scale that has not been seen since the 2013 agreement between Ryan and the Senate Budget Committee’s then-chairman, Sen. Patty Murray (D-Wash.).

Democrats still get to celebrate a messaging victory and will probably take credit for the deal. Sen. Charles E. Schumer (D-N.Y.), a member of leadership, pointed out that the proposal is the kind of spending agreement he and other Democrats have been promoting.

“For months, we Democrats have asked for a budget that increases spending significantly above sequester levels and does so in a way that is equally balanced between defense and key middle-class programs,” Schumer said. “This agreement does both.”

The agreement includes about $80 billion in spending increases over two years, divided equally between defense and domestic programs, with $50 billion in new spending in the first year and $30 billion in the second.

Those increases would be paid for with savings from changes to the Social Security Disability Insurance fund and Medicare payments to doctors and other health-care providers. New revenue would be raised by auctioning off portions of the government-owned broadcast spectrum, selling oil from the strategic oil reserve and cracking down on audits of large business partnerships.

It also includes an additional $16 billion over two years from off-budget spending increases from the Overseas Contingency Operations fund. That portion would not need to be offset, but Democrats previously opposed using the money for defense-only spending. In addition, a premium increase for Medicare Part B recipients would be prevented from going into effect.

Mike DeBonis and Paul Kane contributed to this report.