Opponents of a U.S. Senate bill intended to encourage businesses to share information about cyberthreats may have stalled a vote on the legislation.

Recent news reports had Senate Majority Leader Mitch McConnell pushing for a vote on the Cybersecurity Information Sharing Act (CISA) before a four-week summer recess starting Aug. 10, but a spokesman for the Kentucky Republican said Thursday there were no immediate plans for a vote.

CISA is “one of the bills we want to get done,” however, the spokesman said by email.

CISA would give businesses immunity from customer lawsuits when they share information about cyberthreats with the U.S. Department of Homeland Security, but opponents of the legislation say it would allow businesses to share personal information about customers. DHS could then pass that personal information on to the National Security Agency and other intelligence agencies, critics say.

Supporters of the bill, including several tech trade groups, say CISA would help businesses better respond to cyberattacks by giving them more information about hacker activity.

The Information Technology Industry Council [ITI], a tech trade group, called on the Senate to bring CISA up for a vote, but suggested the bill could be further refined.

“We firmly believe that passing legislation to help increase voluntary cybersecurity threat information sharing ... is an important step Congress can take to enable all stakeholders to address threats, stem losses, and shield their systems, partners and customers,” ITI President and CEO Dean Garfield wrote in a July 23 letter to Senate leaders.

Senators are hearing from constituents opposed to the bill. An old-school fax campaign, launched earlier this week by digital rights group Fight for the Future, has generated more than 6.1 million faxes to senators from constituents opposed to CISA, the group said.

Opponents of CISA also hosted a Q&A on Reddit on Wednesday, with the discussion generating more than 900 comments and an estimated 2 million page views.

The bill includes minimal requirements for businesses to strip out personal information before sharing cyberthreat information with the government, opponents said. Assertions by the bill’s supporters that CISA isn’t a surveillance bill are “highly misleading,” said Jonathan Mayer, a security researcher and lawyer at Stanford University.

CISA “funnels information to the government, private personal data from businesses to the intelligence community,” Mayer said during a press briefing Thursday. In addition, the NSA, using its existing surveillance authority, can use the data to target the people whose information is shared, he said.

“CISA functions as a trigger for existing surveillance authority,” he said. CISA doesn’t need to provide new surveillance authority, “because the government already has cybersecurity surveillance authority.”

In addition to the privacy concerns, opponents say the bill’s provisions allowing businesses to take “defensive measures” against cyberattacks could encourage widespread hack-back attacks against suspected hackers.

Republican leaders in the Senate may attempt to bring CISA to a vote in September, but a delay until then is a victory for opponents, added Senator Ron Wyden, an Oregon Democrat and opponent of the bill. Senators are likely to get an earful from constituents opposed to the bill during the August break, he said during the press briefing.

Lawmakers are under “a lot of pressure to have some kind of response” to cyberattacks after a massive breach at U.S. Office of Personnel Management (OPM) announced in June, Wyden said.

“There is no question in my mind that the federal government needs to step up its game to protect its systems,” Wyden said. “This legislation is the wrong approach.”