Rep. Paul Ryan (R-Wis.) told reporters that the process behind the new budget deal “stinks.” (Melina Mara/The Washington Post)

The House moved closer Tuesday to ending the persistent threat of fiscal crisis that has been a Washington hallmark in recent years, readying a budget deal that would push the next potential spending clashes past the 2016 elections.

The move would empower Rep. Paul Ryan (R-Wis.) as he prepares to take the speaker’s gavel this week by removing some of the land mines that doomed the current speaker.

A vote on the agreement, which would increase federal spending by $80 billion over two years and raise the federal borrowing limit through 2017, is expected Wednesday, shortly after House Republicans meet behind closed doors to nominate Ryan to replace the outgoing speaker, John A. Boehner (R-Ohio).

“This is a good deal,” said Boehner, who will step down Friday. The alternative, he said, would be a debt-ceiling-suspension measure with no guarantee of additional military funding, which most Republicans have advocated.

Many conservatives expressed sharp reservations about the spending agreement, negotiated secretly in recent weeks by Boehner, President Obama and other congressional leaders. But centrist Republicans and Democrats appeared largely united in support, leaving leaders of both parties confident that the bill will pass.

Rep. Paul Ryan (R-Wis.) announced that he would run for House speaker only if his set of demands was met. Washington Post national political reporter Robert Costa explains the conditions and what’s next for Ryan. (Alice Li/The Washington Post)

Senate leaders said Tuesday that they expected to move quickly once the House approved the deal, putting it on Obama’s desk before a Nov. 3 deadline to raise the debt ceiling. “I’m hopeful and optimistic that that bill will come over to the Senate, and when it does, we’ll take it up,” said Majority Leader Mitch McConnell (R-Ky.).

But the most closely watched player on Capitol Hill on Tuesday was Ryan, who walked a fine line between appeasing the conservative lawmakers he will routinely have to corral in his new job and endorsing the budget legislation, which those conservatives oppose.

He did so by making a distinction between the substance of the deal and the way in which it was struck: “I think this process stinks,” Ryan told reporters Tuesday. “Under new management, we are not going to run the House this way.”

That message appears calibrated to avoid alienating GOP lawmakers who have pressed for a more bottom-up approach to House management. But Ryan also steered clear of the deal’s specifics, which are deeply unsettling to House conservatives and largely similar to the provisions of a deal Ryan struck two years ago with Obama and Senate Democrats.

The approach appeared to be working Tuesday, with most conservative Republicans saying they did not blame Ryan for the shortcomings of the new agreement.

Lawmakers are set to vote on outgoing House Speaker John Boehner’s plan to avert another government shutdown and raise the debt ceiling. Here’s what you need to know about it. (Sarah Parnass/The Washington Post)

“This is John Boehner’s deal,” said Rep. Ken Buck (Colo.), a conservative freshman and a member of the hard-right House Freedom Caucus.

Rep. John Fleming (R-La.), another Freedom Caucus member, said that Ryan “promises a much more orderly and grass-roots process from the ground up, an organic type of process, and we’re going to take him at his word.”

“He’s made those commitments in private, that he’s not going to drop a big bill like this on us at the last minute and expect us to vote for it,” Fleming added.

If those feelings persist, the budget deal could pass the House on Wednesday with votes from centrist Republicans and Democrats, while allowing Ryan to win the speaker’s chair Thursday with both a united GOP and a clean fiscal slate.

But other pitfalls appeared Tuesday for the budget accord. The agreement includes several controversial measures, such as reductions in crop insurance payments and the repeal of an Obamacare provision that requires large companies to automatically enroll full-time employees in a health plan.

And while Republican leaders originally said all spending increases would be fully offset with savings, the Congressional Budget Office estimated Tuesday that the savings would fall about $5 billion short. That had key players scrambling into the night to resolve those issues to avoid losing more GOP support.

Still, most Democrats and many Republicans said the bill reflected a reasonable compromise.

The deal was close to a complete victory for Democrats, who had pushed for spending increases for months. House Minority Leader Nancy Pelosi (D-Calif.) embraced the agreement early Tuesday, signaling that the 188 House Democrats could provide a large portion of the vote needed Wednesday.

If so, Boehner will have to win the support of just 40 to 50 Republicans to pass the deal. Many of those votes are expected to come from defense hawks who pressed for the military spending increases included in the bill.

“A two-year deal will provide the Department of Defense with the certainty it needs to plan for and execute its missions around the world,” Rep. Michael R. Turner (R-Ohio) wrote to a group of more than 100 pro-military Republicans, urging them to support the legislation.

Rep. Tom Cole (R-Okla.) said the deal includes other significant wins for Republicans, including long-term reforms to Social Security and Medicare.

The $80 billion increase, split between defense and nondefense spending, would be offset by savings from changes to the Social Security Disability Insurance trust fund and reductions in Medicare payments to health-care providers. Additional revenue would be raised by auctioning off new portions of the broadcast spectrum, selling part of the Strategic Petroleum Reserve and redoubling audits of large business partnerships.

“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.”

Ryan has not yet said how he plans to vote on the budget package. Supporting it could refracture House Republicans less than a week after Ryan appeared to have largely healed the split between hard-line conservatives and the rest of the conference. On the other hand, opposing it could open Ryan to charges of political opportunism.

The deal shares more than a name — the Bipartisan Budget Act — with the 2013 accord that Ryan struck with Sen. Patty Murray (D-Wash.). At the time, both lawmakers chaired their respective chambers’ budget committees.

Both deals were meticulously negotiated behind closed doors and increased federal spending in the short term in exchange for potential future savings through modest reforms to entitlement programs.

Boehner himself said Tuesday that the new deal “isn’t a whole lot different” from the 2013 pact and made clear that he believed it will ease Ryan’s burden over the next 18 months, probably sparing him from multiple threats of federal shutdowns or defaults.

“This will make it easier for the entire Congress for the balance of this year, and it’ll make next year a whole lot smoother for the Congress as well,” Boehner said.