After weeks of tense wrangling between the White House and House Republicans, the tax deal reached Saturday to raise the debt ceiling and curtail federal spending bolsters President Biden’s argument that he is the only figure still it can be bipartisan in a deeply partisan era.

But it comes at the cost of irritating many in his own party who have little appetite for meeting Republicans in the middle and think the president can’t help but give too much away in an eternally short-lived search for consensus. And now he will test his influence over his fellow Democrats, he will need to pass the deal in Congress.

The deal-in-principle he reached with President Kevin McCarthy represents a case study in the governance of a Biden presidency, underscoring the fundamental tension in his leadership since the 2020 primary, when he bested his progressive rivals to win the nomination. democrat. Mr. Biden believes in his bones to cross the aisle even at the expense of some of his own priorities.

It has repeatedly demonstrated this since it was inaugurated two and a half years ago, even as skeptics doubted that a cross-party deal was still possible. In particular, he pushed through Congress a bipartisan public works program that allocates $1 trillion to build or repair highways, bridges, airports, broadband, and other infrastructure; legislation expanding treatment for veterans exposed to toxic combustion pits; and an investment program to boost the nation’s semiconductor industry, all of which passed with Republican votes.

However, this is not a time when bipartisanship is valued like when Biden came to the Senate in the 1970s, 1980s and 1990s. His desire to position himself as the leader who can unite a deeply divided country is at the core of his case for a second term next year. But he conflicts with the interests of many Democrats who see more political benefits in standing strong against former President Donald J. Trump’s GOP and prefer to draw a starker contrast for their own 2024 election when they hope to win back the House.

“The deal represents a compromise, which means not everyone gets what they want,” Biden said in a written statement issued Saturday night as the deal was being announced. “That is the responsibility of governing.”

Most important from Biden’s point of view, the deal averts a catastrophic national default that could have cost many jobs, tanked stock markets, jeopardized Social Security payments and sent the economy into reeling. He is banking on the assumption that Americans will appreciate mature leadership that doesn’t gamble with the nation’s economic health.

But many on the political left are upset that, in their view, Mr. Biden caved in to Mr. McCarthy’s hostage-taking strategy. The president who said the debt ceiling was “non-negotiable” ended up negotiating it after all to avoid a national default, and he hardly cared for the fiction that the spending cap talks were somehow separate.

Liberals were pressuring Biden to toughen up Republicans and short-circuit the debt ceiling by claiming the power to ignore it under the 14th Amendment, which says the federal government’s “validity of public debt” is “not to be questioned.” . But while Mr. Biden agreed with the constitutional interpretation, he concluded that it was too risky because the nation could still go into default while the issue was litigated in court.

And so, much to the chagrin of his allies, the negotiation of the last few weeks was entirely on Republican terms. While details were still emerging this weekend, the final agreement did not include any new tax initiatives from Biden, such as higher taxes for the wealthy or deeper discounts for insulin. The question was essentially how much of the Cap, Save and Growth Act passed by House Republicans last month the president would accept in exchange for raising the debt ceiling.

But Mr. Biden managed to strip the Limit, Save and Grow Act significantly of what it originally was, much to the dismay of conservative Republicans. Instead of raising the debt ceiling for less than a year while imposing strict ceilings on discretionary spending for 10 years, the agreement ties the two so that the spending limits last only two years, as does the increase in the debt ceiling. Debt. While Republicans insisted on predicating caps on a baseline of 2022 spending levels, the appropriations adjustments will make it effectively equivalent to the more favorable 2023 baseline.

As a result, the deal will reduce anticipated spending over the decade to just a fraction of what the Republicans were seeking. The Congressional Budget Office estimated that the limits passed by House Republicans last month would have cut $3.2 trillion in discretionary spending over 10 years; a New York Times estimate suggests the deal struck by Biden and McCarthy could cut just $650 billion instead.

Furthermore, while Biden did not advance many new Democratic policy goals in the McCarthy deal, he effectively shielded most of his gains from the first two years of his presidency from Republican efforts to gut them.

The Republican plan called for repealing many of the clean energy incentives Mr. Biden included in the Cut Inflation Act, cutting additional funding for the Internal Revenue Service to go after the wealthy who cheat on taxes, and blocking the president’s plan. to forgive $400 billion in student loans for millions of Americans. None of that was in the final package.

In fact, the IRS provision offers an example of Mr. Biden’s bargaining. As a token concession to Republicans, he agreed to cut about $10 billion of the additional $80 billion previously allotted to the agency, but most of that money will be used to prevent deeper cuts in Republican-sought discretionary spending.

One of the most sensitive areas for Biden’s progressive allies was the Republican insistence on imposing or expanding work requirements on recipients of social safety net programs, including Medicaid, food assistance and welfare payments for families. Biden, who supported work requirements on welfare in the 1990s, was initially open to considering Republican proposals, only to face fierce pushback from Democrats.

On Friday night, even as the deal was being finalized, the White House issued a harsh statement accusing Republicans of trying to “take food out of hungry Americans’ mouths” while preserving tax cuts for the rich, a barrage intended as much to reassure restless liberals attack hardline conservatives.

The final agreement between Mr. Biden and Mr. McCarthy does not include work requirements for Medicaid, but raises the age of people who must work to receive food assistance through the Supplemental Nutrition Assistance Program, or SNAP, to 54, while eliminating requirements for veterans and homeless people. The agreement relaxes Republican provisions to expand the work requirements for Temporary Assistance for Needy Families.

The challenge now for Biden is to sell the compromise to his fellow Democrats. Just as McCarthy knows he will potentially lose dozens of disappointed Republicans over the adaptations he made, the president expects many in his own party to vote against the final product as well. But he needs to deliver enough Democrats to make up for defections from the GOP to carve out a bipartisan majority.

Minutes after the deal was announced Saturday night, the White House sent out briefing materials and talking points to all House Democrats and followed up with phone calls Sunday. “Negotiations require give and take,” the talking points read. “Nobody gets everything they want. This is how divided government works. But the president successfully protected his and the Democrats’ top priorities and the historic economic progress we’ve made in the last two years.”

Mr. Biden has been here before. As vice president, he was President Barack Obama’s chief negotiator in various tax battles, but so riled up his fellow Democrats that they thought he had given away too much that Sen. Harry M. Reid of Nevada, then the Senate party leader, effectively barred the Mr. Biden in 2013 of the negotiations on an increase in the debt ceiling.

Kicking a vice president out of the room, of course, is one thing. Mr. Biden is now the president and the leader of his party heading into a re-election year. It’s his room. And he’s handling it on his own terms, whether he likes it or not.