House Republican leaders negotiated their way through fierce intraparty opposition and passed on Wednesday one of the three key pieces of legislation on their agenda for the week, but their struggles are far from over.

The bill that passed, a three-year reauthorization of a foreign surveillance law that expires Thursday, cannot clear the Senate.

The Senate is discussing sending the House back a short-term extension of Section 702 of the Foreign Intelligence Surveillance Act to buy more time for negotiations that have already run past the initial deadline.

The House will likely pass the short-term extension, but Republican leaders there are not eager to go back to the drawing board on the terms of a longer-term FISA reauthorization after reaching a fragile compromise.

The FISA bill passed on a 235-191 vote. While 22 Republicans voted in opposition, that was more than offset by the 42 Democrats who supported the bill.

The lower chamber was also set to concur with the Senate in approving a budget resolution needed to kickstart the filibuster-proof reconciliation process Republicans plan to use to fund immigration enforcement agencies through the remainder of Mr. Trump’s presidency.

However, that vote was held open Wednesday evening as Republican leaders negotiated with lawmakers on a farm bill reauthorization they also planned to pass this week.

“This is why they say lawmaking is like watching sausage being made. That’s what this is. But we’ll get it done,” House Speaker Mike Johnson, Louisiana Republican, told reporters as he headed into a “family meeting” over the farm bill.

Earlier Wednesday, Mr. Johnson and his leadership team had spent two hours on the floor arm-twisting Republicans just to back the procedural rule needed to begin debate on all of the aforementioned bills.

Eight Republicans had at one point cast votes against the rule, but Republican leaders ultimately flipped them all to yes.

“We have the smallest margin conceivable, one of the smallest in the history of the United States Congress, so it takes time,” the speaker said of the Republican majority’s current two-vote margin.

To secure the votes for the rule, Republican leaders told the holdouts that consideration of the farm bill would be delayed until issues over that measure and an ethanol fuel bill Republicans were trying to tie to it were resolved.

Several farm-state lawmakers convinced leadership to change the plan to proceed with the farm bill vote this week and hold off on the bill to allow year-round sales of E15, an ethanol-gasoline fuel blend.

The pivot angered other lawmakers who thought they would have more time to debate the farm bill, as members still wanted to see other changes to the measure.

“Anything I say right now will not be good,” Rep. Chip Roy, Texas Republican, said after a confrontation with Mr. Johnson over the changing plans, calling the multi-layered legislative negotiations a “dump.”

Mr. Johnson is also struggling to get on the same page as Senate Republican leaders on multiple legislative issues.

The speaker approved a procedural maneuver to add separate legislation to ban the Federal Reserve from issuing a central bank digital currency, or CBDC, to the FISA measure before it is sent to the Senate.

Senate Majority Leader John Thune warned the CBDC ban would be “dead on arrival” in his chamber, but House leaders proceeded anyway.

It was a key concession for conservatives, particularly members of the House Freedom Caucus, who argue CBDCs could be used to spy on Americans as China has done with its state-backed digital currency.

“It’s arguably more dangerous than FISA,” Rep. Andrew Clyde, Georgia Republican, said of why the CBDC ban was key to earning his support.

The Senate previously passed a five-year moratorium on CBDCs as part of a housing package that is stalled in the House, but a permanent ban is a bridge too far for most Senate Democrats whose votes are needed because of the upper chamber’s filibuster rules.

Mr. Thune said another short-term FISA reauthorization will likely be needed because of the disagreements between the two chambers.

That would give privacy advocates in both parties more time to make their case for a provision requiring executive officials to obtain a judicial warrant before accessing Americans’ data swept up in foreign surveillance.

The House-passed bill does not include a warrant requirement but adds new restrictions on searching a database of information obtained under the Section 702 authority for U.S. persons.

It also includes new oversight provisions and criminal penalties for abuses of the surveillance authority.

Sen. Tom Cotton, Arkansas Republican and chairman of the Senate Select Committee on Intelligence, had been shopping his own FISA reauthorization proposal around the upper chamber but has yet to secure a deal with Democrats.

Sen. Ron Wyden, Oregon Democrat and a proponent of adding a judicial warrant requirement to Section 702, said the House FISA bill and Mr. Cotton’s proposal are both “deeply flawed.”

“So there’s two bills that go in the wrong direction,” he said.

Sen. Lindsey Graham, South Carolina Republican, scoffed at a judicial warrant requirement, saying, “We’re not solving crimes. We’re investigating potential national security threats, so a warrant wouldn’t be required.”

President Trump has called for a clean extension of existing law, arguing the surveillance authority FISA provides is essential to national security despite past abuses against him and his allies.