A measure to expand FBI surveillance power appears to have the support needed to pass the Senate, but with a second vote not yet imminent privacy activists are working to flip senators so the amendment’s dramatic one-vote defeat last week does not become equally narrow passage.

Senate leaders have not yet scheduled a re-vote, but with Sen. Dianne Feinstein, D-Calif., being one of four senators who were absent for the first vote there’s an expectation the legislation could pass.

Feinstein was in California on Wednesday when the measure failed to reach the 60 votes needed to end debate. Though her office was unable to confirm her position, in May she voted for a similar amendment in the Senate intelligence committee, and she’s generally considered one of the most hawkish senators on surveillance issues.

The offices of the other absent senators – Bob Menendez, D-N.J.; Mike Crapo, R-Idaho; and Joe Donnelly, D-Ind. – were unable to provide U.S. News information on their stances and are being targeted by activists.

The surveillance amendment would expand what the FBI can take with a national security letter (NSL) to include online records including browsing histories and email metadata -- a category called “electronic communications transactional records” or ECTRs.

The FBI previously demanded these records – until at least 2013 – using NSLs, despite a 2008 Justice Department Office of Legal Counsel opinion that found no legal grounds for compelled disclosure. Increased tech industry pushback resulted in the FBI’s request for the current amendment.

NSLs are issued when the FBI claims records sought may be relevant to an investigation into terrorism or espionage, but the letters are controversial because they do not require a judge's approval and often come with an open-ended gag order on companies involved.

Amendment critics say the FBI currently can get ECTR records if a judge agrees there's sufficient reason and that in emergencies authorities can, pursuant to the recently enacted USA Freedom Act, demand the records and seek retroactive court approval.

Still, privacy advocates found the political wind against them after the deadliest mass shooting in modern U.S. history this month, committed by a U.S. citizen who pledged allegiance to the Islamic State group as he murdered 49 people at a gay nightclub.

There were surprises in the original amendment vote. Sen. Ted Cruz, R-Texas, voted in favor, despite a history of speaking in favor of protections against government surveillance. He released a statement standing by his vote.

And Alaska Sen. Dan Sullivan, another Republican, switched his vote to “yes” as the amendment came within striking distance of passing, with opponents speculating leadership arm-twisting was involved.

In a statement to U.S. News, Sullivan’s office says he intends to vote in favor of cloture again, but that he’s not sure he will support the bill in a subsequent up-or-down vote, which requires just 50 votes for passage.

"Senator Sullivan had some concerns about the amendment and continues to," spokesman Mike Anderson says. "But after further discussions with his colleagues, and given the importance of the issue, he ultimately believes that this amendment deserves an up-or-down vote."

That stance is not acceptable to privacy advocates who hope to corral enough constituent pressure to kill the measure. If Feinstein votes as expected, opponents likely need to break off one cloture supporter along with convincing all three absentees.

“If they vote for cloture they’re supporting the amendment and there’s no excuse for that,” says Sean Vitka, legislative counsel at Fight for the Future, a group that allows activists to dial both their senators through the website decidethefuture.org.

So far, he says, more than 2,500 calls have been placed to Senate offices, driven by email blasts. Vitka says the group will respond as forcefully and quickly as possible to summon more grass-roots pressure if it learns a second cloture vote is scheduled.

“It basically can come up at any time with very little heads up,” Vitka says.

Another pressure group, Credo Action, recorded more than 1,300 calls as of Tuesday afternoon for a drive it launched Monday to convince senators to vote "no."

"CREDO activists in 12 states are making calls to one of their senators today in opposition to the amendment," says Josh Nelson, campaign manager for Credo Action.

That group is specifically targeting Menendez, Crapo and Donnelly, as well as Cruz, Sullivan and Sens. Ron Johnson, R-Wis.; Bob Casey, D-Pa.; Mark Kirk, R-Ill.; Jack Reed, D-R.I.; Amy Klobuchar, D-Minn.; Harry Reid, D-Nev.; and Jeff Flake, R-Ariz.

Other groups involved in lobbying against the amendment have asked constituents to call senators, including the American Civil Liberties Union, whose plea on Twitter last week was retweeted 1,300 times, including by whistleblower Edward Snowden, who after years of legislative surveillance expansions in 2013 leaked documents that turned the tables.

Spokespeople for the offices of Senate Majority Leader Mitch McConnell, R-Ky., and Senate Majority Whip John Cornyn, R-Texas, said Tuesday that there’s no decision yet on when the revote will happen.

That's potentially significant as the clock ticks before the Senate on Friday begins a short recess for the Fourth of July. The Senate then will be in session for two weeks before a long August recess that reaches into September.

It's unclear if the amendment can pass the House of Representatives, but even if the pending measure is defeated, privacy advocates still will have to fight to excise similar wording from a committee-passed intelligence authorization bill.

One of the most vocal Senate privacy advocates, Sen. Ron Wyden, D-Ore., on Monday placed a hold on the authorization bill, which slows the process and requires regular order for legislation, including standard cloture, amendment-filing and voting processes.

Keith Chu, a spokesman for Wyden, says it's possible amendment supporters "could still try to ram it through at some point," though this week is appearing less of a possibility.

Some backers of the amendment, such as Sen. Richard Burr, R-N.C., said during debate last week there's no evidence the new authority would have aided the FBI when it had investigated the Orlando shooter in 2013 and 2014. He cast the possible reform as a matter of efficiency to cut a court-approval process he said could take a month. But Cornyn, the measure's most forceful advocate, argued such collection could well have revealed gunman Omar Mateen had been looking online at radical sermons.

Nicholas Merrill, the owner of now-defunct Calyx Internet Access who in November became one of the first people given permission by a court to speak freely about receiving a NSL for customer information, said last week the public should consider the past excesses of the FBI.

“The fact that the government is now attempting to legalize the demand for electronic communications transactional records that they demanded of me back in 2004 is a tacit admission that what they did with all of the roughly 500,000 NSLs issued since then was illegal and overreaching,” Merrill said.