Senators on the intelligence committee expressed deep doubts about curbing the National Security Agency's broad data collection powers as the upper legislative chamber begins to consider a landmark surveillance bill that passed the House last month.

Lawmakers attacked the USA Freedom Act as insufficiently protective of both privacy and national security as intelligence and law enforcement officials, who now back the bill, conceded that under its provisions they would still have access to a large amount of US phone and other data.

Deputy attorney general James Cole told the Senate intelligence committee on Tuesday that the bill allows the NSA to collect information "two hops", or degrees removed from a targeted phone account. "It gives us the prospective collection, it gives us a wider range of information that we wouldn't have under normal authorities," he said.

That account bothered three Democratic privacy advocates on the panel – Oregon's Ron Wyden, Colorado's Mark Udall and New Mexico's Martin Heinrich – but most of the consternation shown by the panel came from the opposite direction, indicating that a surveillance bill whose privacy protections have been largely weakened will still face a difficult road in the Senate.

The panel's leaders, Democrat Dianne Feinstein of California and Republican Saxby Chambliss of Georgia – both of whom remain staunch advocates of the bulk domestic phone metadata collection that the bill is aimed at ending – feared that restricting the volume of data to which the NSA has access will leave the US vulnerable to a terrorist attack.

In some cases, the panel, charged with overseeing the intelligence agencies and preventing abuse, advocated greater authorities for the surveillance agency than the NSA itself requested.

The panel's leaders sparred with Verizon vice-president Michael Woods, who reiterated his industry's opposition to legislation ordering telecoms to keep retain customer records beyond present practice of an 18-month maximum – something NSA deputy director Rick Ledgett said the agency did not consider necessary.

But Chambliss and Feinstein were wary of allowing the companies the discretion to set their own data retention requirements, out of fear it would leave NSA effectively blinded.

Republican senator Saxby Chambliss has called to delay changes to the NSA surveillance programs. Photograph: Tami Chappell/Reuters

"Things are going to change five years from now or three years from now," Chambliss said.

"If there's not some requirement to be kept for some period of time, then we may as well not have this program. We will lose it and we will lose the ability to interrupt, disrupt terrorist activities."

A former panel chairman, Democrat Jay Rockefeller of West Virginia, was skeptical of the idea of abridging the bulk phone data surveillance at all.

"We're doing something unnecessary and unpredictable here, which might make the public feel better, but would not be good for national security, which is what our job is," Rockefeller said.

But uniting critics and advocates of the surveillance was a dissatisfaction with fundamental language in the USA Freedom Act stipulating the very things that the government may collect.

The phrase "specific selection term", a basic definition of the sort of things a government request for data collection must specify, came under criticism for being both too broad, too narrow and too vague.

"The problem comes with the definition of a 'specific selection term', which is not clear on its face, and I believe it is confusing," Feinstein said.

Democratic senators Ron Wyden and Mark Udall, and on the right, Democrat Richard Blumenthal, with Republican Rand Paul, discussing the NSA reform bill. Photograph: Mark Wilson/Getty Images

After the USA Freedom Act passed two House committees in May, intelligence community lawyers negotiated a broadening of the definition before the bill reached the House floor. It helped ensure passage on a 303-121 vote, but cost the support of many of the bill's advocates in and outside of Congress, who warned it will no longer end the bulk records collection exposed a year ago thanks to leaks by Edward Snowden.

Harley Geiger of the Center for Democracy and Technology told the panel that there was nothing statutorily preventing NSA from specifying "Verizon or Gmail.com or the state of George as a specific selection term."

"Let us not use the phrase 'bulk collection' as coded jargon for existing programs or nationwide surveillance dragnets," Geiger continued. "Bulk collection, as any normal person would understand it, means the large scale collection of information about individuals with no connection to a crime or investigation. In that respect, the bill does not end bulk collection."

Cole said that under the USA Freedom Act, the NSA could no longer engage in "indiscriminate" phone data collection, although he was quick to insist that over a decade of NSA engaging in precisely that was not itself abusive.

"Certainly, if you went to collect all the telephone records within a certain zip code, indiscriminately, that would be prohibited, because the point of this is to limit and to focus," Cole said.

Udall urged a tightening of the bill's language.

"The NSA has shown time and time again it will seize on any wiggle room in the law, and there is plenty of that in this bill," he said.