After the House’s lopsided bipartisan vote to end the National Security Agency’s bulk collection of Americans’ phone records, the Senate is under considerable pressure to pass a similar measure. If it doesn’t, lawmakers risk letting the authority to collect the records expire June 1, along with other important counterterrorism provisions.

The House bill, known as the USA Freedom Act, would replace bulk collection with a system to search the data held by telephone companies on a case-by-case basis. It passed 338-88.

In the Senate, however, the legislation faces a 60-vote hurdle to begin debate. A similar bill failed to do so last year after passing the House by a wide margin. And the Senate majority leader, Republican Mitch McConnell, has expressed his opposition to the current House bill.

What’s different this year, though, is that if Congress doesn’t act, three provisions will expire. Not just the law authorizing the bulk collection of phone records, but also a measure allowing so-called roving wiretaps, which the FBI uses for criminals who frequently switch cell phones. A third provision makes it easier to obtain a warrant to target a “lone wolf” terror suspect who has no provable links to a terrorist organization.

McConnell has said he will put a bill on the floor to reauthorize all three provisions without changes. But Wednesday’s vote suggests the House won’t pass such a bill, said Rep. Adam Schiff, the ranking Democrat on the House Intelligence Committee.

“The overwhelming support for the House measure should show Senate leaders that a straight re-authorization … is a nonstarter in the House,” Schiff said, “and the time to move forward on these vital reforms is now, not after the statutory deadline passes.”

McConnell has said he is open to a compromise. If one materializes, and something close to the House bill becomes law, it would represent one of the most significant changes stemming from the unauthorized disclosures of former NSA contractor Edward Snowden.

President Barack Obama supports the House legislation, known as the USA Freedom Act, which is in line with a proposal he made last March.

The issue also has implications for the 2016 presidential contest, with Republican candidates staking out different positions.

The revelation that the NSA had for years been secretly collecting all records of U.S. landline phone calls was among the most controversial disclosures by Snowden, who in 2013 leaked thousands of secret documents to journalists. The program collects the number called, along with the date, time and duration of call, but not the content or people’s names. It stores the information in an NSA database that a small number of analysts query for matches against the phone numbers of known terrorists abroad, hunting for domestic connections to plots.

Officials acknowledge the program has never foiled a terrorist attack, and some within the NSA had proposed abandoning it even before it leaked — on the grounds that its financial and privacy costs outweighed its counterterrorism benefits.

Proponents of keeping the program the way it is argue that the rise of the Islamic State group, and its efforts to inspire Westerners to attack in their own countries, make it more important than ever for the NSA and FBI to have such phone records at their disposal to map potential terrorist cells when new information surfaces. And they say there is no evidence the program has ever been misused.

Under the House measure, the NSA would no longer collect and store the records, but the government still could obtain a court order to obtain data connected to a specific number from the phone companies, which typically store them for 18 months.

The House measure also provides for a panel of experts to advocate for privacy and civil liberties before the secret intelligence court that oversees surveillance programs. And it allows the government to continue eavesdropping on foreign terrorists without a warrant for 72 hours after they enter the U.S., giving authorities time to obtain a warrant.

On Tuesday, NSA Director Adm. Mike Rogers and FBI Director Jim Comey briefedsenators on the program. Afterward, Republican Sen. Bob Corker of Tennessee, the chairman of the Foreign Relations Committee, told reporters the NSA was not collecting all the data it should be. He declined to be specific, saying the briefing was classified, but he appeared to be addressing the fact that the collection does not include most mobile calls in an era when many people have stopped using landlines.

“The way it’s being implemented today, I don’t see how it’s … useful at all to the American people,” said Corker, who wants to reauthorize the current law. “And I’m shocked, shocked … by the small amount of data that is even part of the program. It needs to be ramped up.”

U.S. officials have confirmed the mobile records gap, saying it stemmed from technical and policy issues that ultimately would have been addressed absent the Snowden leak.Under the House’s USA Freedom Act, they said, the NSA would expand its queries to include mobile records, creating a potentially more effective program. But they have expressed concerns about working out an arrangement with phone providers to standardize the data so the information can quickly be searched.

Those officials, not authorized to comment publicly by name, spoke only on condition of anonymity.