The annual defense bill has become entangled in a tumultuous Republican feud in the House, as hard-right lawmakers revolt over a bipartisan agreement to jettison a raft of deeply partisan dictates that would have limited abortion access, transgender care and diversity training.

The dispute over the $886 billion military policy bill, considered one of the few pieces of legislation Congress is obligated to pass every year, is unlikely to sink the legislation altogether. But it has created a political crisis for Speaker Mike Johnson, who has come under withering criticism from ultraconservative Republicans for his handling of government spending measures and now faces a backlash over what is normally a broadly popular bill.

“It’s going to be a very big problem for him if he puts it on the floor. Our base will be furious,” said Representative Marjorie Taylor Greene, Republican of Georgia, said of the defense bill. She excoriated Mr. Johnson for having given up on a litany of policy changes conservatives had championed, adding, “He’s going to lose support.”

The bill has been a lightning rod for controversy since this summer, when House Republicans, under pressure from the far right to combat what they charged was “wokeness” in the military, packed it with measures to roll back abortion access, health care for transgender service members and diversity, equity and inclusion training. The result was a rawly partisan bill that passed the House largely along party lines, a rarity for the defense policy bill, which traditionally draws lopsided bipartisan backing.

But Democrat-led Senate passed a far more restrained version, and in closed-door talks between then two chambers, House negotiators abandoned almost all of their most extreme policy dictates. The compromise package, which was released late Wednesday, prompted cries of betrayal by right-wing Republicans, who were further incensed to discover that it included an extension of a warrantless surveillance program many of them believe has been abused to spy on Americans.

Now Mr. Johnson is bracing for a rebellion over the bill on the right that is all but unavoidable. House action is expected later this month, after approval of the legislation in the Senate, which took its first steps on Thursday toward considering it.

Mr. Johnson, a Louisiana Republican who was elected speaker in October, is keenly aware that his predecessor was ousted by Republican hard-liners angry that he had cut deals with Democrats, and who believed he had not catered enough to the demands of his conservative base. In theory, he could face the same fate under House rules that allow a single lawmaker to call a snap vote to remove the speaker, though Republicans appear to have no appetite for a repeat of the damaging episode.

Mr. Johnson, a staunch conservative, initially enjoyed a measure of leeway from right-wing lawmakers who always distrusted and disliked former Speaker Kevin McCarthy. Last month, many of them argued that the new speaker deserved time to get his bearings, and mostly refrained from criticizing him for working with Democrats to pass a stopgap spending measure to avert a government shutdown that lacked any of the spending cuts or policy changes they wanted.

But their response to the defense bill compromise suggests they are losing patience with Mr. Johnson.

“I would say that this is a building block,” said Representative Eli Crane, Republican of Arizona, one of the eight Republicans who voted to oust Mr. McCarthy. “It leads to more disappointment.”

A spokesman for Mr. Johnson did not respond to a request for comment. But several House Republicans defended him, arguing that the hard-liners’ demands were unrealistic.

“We voted for this package knowing that things would be stripped out in the Senate,” Representative Michael McCaul, Republican of Texas and chairman of the Foreign Affairs Committee. “I’ve been doing this long enough to know it wouldn’t be in the final” bill.

Congress has passed an annual military policy bill for more than six decades running, and members of both parties believe that Mr. Johnson will be able to help maintain that streak. On Thursday, the Senate voted to begin debating the compromise defense bill; the House is expected to follow suit as soon as next week.

Another major challenge to passage may come from the last-minute addition of a short-term extension of a surveillance law known as Section 702 that allows the government to collect the communications of foreigners abroad without warrants — even when the targets are speaking with Americans.

More than 50 Republicans and Democrats signed a letter last week arguing that it would be irresponsible to extend the program without significant changes. This week the House Judiciary and Intelligence committees each passed, on a bipartisan basis, rival bills to limit the program. The defense bill would extend it through April 19, 2024, to buy lawmakers more time to iron out differences between the competing bills.

But because of a quirk in how Congress wrote the law creating it, that seemingly short extension could actually keep the program alive into 2025.

The addition of the Section 702 extension prompted a wave of new recriminations from conservatives Thursday, who pledged to try to rally votes against the bill.

“I will have to more than oppose it,” Representative Chip Roy, Republican of Texas, said in a post on social media, in response to a senator stating his opposition to the extension. Mr. Roy, a member of the Freedom Caucus, sits on the Rules Committee, which controls what legislation comes to the House floor, and in what form.

Some Republicans are also angry that the bill does not address the Pentagon’s policy of allowing service members to take leave and be reimbursed for transportation expenses if they must travel to obtain an abortion or certain fertility treatments because such procedures are not available where they are based. The policy was created after the Supreme Court struck down Roe v. Wade, leaving the nation with a patchwork of state abortion laws.

The legislation also omits a House-passed provision to limit transgender health services available to military members and their families.

The bill does, however, include limited restrictions on diversity initiatives, including a cap on salaries and hiring for positions devoted exclusively to such training programs, and a ban on teaching critical race theory in military academies and schools. It also includes a ban on requiring Defense Department personnel to identify themselves by their preferred pronouns, and a ban on official displays of “unapproved” flags — including banners signaling L.G.B.T.Q. pride.

Republicans also secured provisions establishing a review board to consider reinstatement petitions from service members let go for refusing to comply with the military’s now-defunct Covid-19 vaccine mandate and a special inspector general’s office to monitor how U.S. military assistance to Ukraine is being used.

The bill maintains a program to send Ukraine $300 million annually for the next two years, however, despite a majority of House Republicans having voted against that program this fall.

Charlie Savage contributed reporting.