Lawmakers of both parties expressed deep skepticism Wednesday about the government’s bulk collection of Americans’ telephone records and threatened not to renew the legislative authority that has been used to sanction a program described as “off the tracks legally.”

The backlash appeared to focus on the concern that the Obama administration’s interpretation of its powers far exceeds what lawmakers intended. At a hearing of the House Judiciary Committee, lawmakers forcefully pressed officials from the National Security Agency, the Justice Department, the FBI and the Office of the Director of National Intelligence to justify the government’s collection and storage of the communications records of vast numbers of Americans.

“This is unsustainable, it’s outrageous and must be stopped immediately,” said Rep. John Con­yers Jr. (Mich.), the highest-ranking Democrat on the panel.

Rep. F. James Sensenbrenner Jr. (R-Wis.) — who sponsored the USA Patriot Act, which ostensibly authorized the collection — warned that the House might not renew Section 215 of the act, a key provision that gives the government its authority.

“You’ve got to change how you operate 215 . . . or you’re not going to have it anymore,” Sensenbrenner said.

The sharp and sometimes angry questioning stood in stark contrast to the tone of hearings on the surveillance programs by congressional intelligence committees in recent weeks. It also came as the government faces a growing number of legal challenges to its collection of “metadata” — information about the numbers Americans called, the date and time of the calls, and how long the calls lasted.

Intelligence officials insist that the program operates under tight guidelines and is overseen by the Foreign Intelligence Surveillance Court. They also stressed that the collection efforts have proved crucial to disrupting terrorist plots.

Although questions about the program remain, administration officials offered new details about the methodology used to analyze the data. For the first time, they suggested that when the government queries its database of phone records — as it did 300 times last year — it probably is looking at the phone records of huge numbers of individuals.

“The court has approved us to go out two or three ‘hops,’ ” NSA Deputy Director John C. Inglis said. “And it’s often at the second hop” that information is gained that leads the FBI to investigate the person’s contacts further.

A “hop” refers to the way in which analysts broaden their analysis. When analysts think they have cause to suspect an individual, they will look at everyone that person has contacted, called the first hop away from the target. Then, in a series of exponential ripples, they look at everyone all those secondary people communicated with. And from that pool, they look at everyone those tertiary people contacted. This is called a second and a third hop.

Jameel Jaffer, deputy legal director at the American Civil Liberties Union, said that the NSA has been trying to make it seem as though it peeks at the communications of a tiny subset of people, but that with such hops, it has reviewed the communication patterns of millions.

“The first hop takes you to 100 people” the person called, Jaffer said. “The second one takes you to 10,000. The third one takes you to a million.”

The ACLU was one of more than 50 signatories of a letter to be sent to President Obama and congressional leaders Thursday calling for more disclosure about the scale of government surveillance requests to technology and telecommunications companies.

Lawmakers said the surveillance effort, which was disclosed by former NSA contractor Edward Snowden , is too broad and intrusive.

“I think very clearly this program has gone off the tracks legally and needs to be reined in,” said Rep. Zoe Lofgren (D-Calif.).

Deputy Attorney General James M. Cole said collected information does “not include names or other personal identifying information” and does not include the content of any phone calls. He added that the records are not protected by the Fourth Amendment.

Several lawmakers disagreed.

“I maintain that the Fourth Amendment — to be free from unreasonable search and seizure — means that this metadata collected in such a super-aggregated fashion can amount to a Fourth Amendment violation before you do anything else,” Conyers said.

A second program, code-named PRISM, by contrast, “does collect content of communications,” Cole said, but it is aimed at non-Americans who are “reasonably believed to be overseas.” The content of communications such as phone calls and e-mails can be gathered when one person in the exchange is in the United States, provided that the communication was initiated by “a non-U.S. person, outside the United States,” he said.

A practice known as “reverse targeting,” or indirectly obtaining Americans’ communications by targeting foreigners located overseas, is explicitly prohibited, Cole said.

Cole said the programs are legal and overseen by the Foreign Intelligence Surveillance Court. He also said the programs “achieved the right balance” between protecting Americans’ safety and their privacy.

“Both programs are conducted under laws passed by Congress,” Cole said.

The 11 judges on the secret FISA court that approves surveillance “are far from rubber stamps,” he said. “They don’t sign off until they are satisfied that we have met all statutory and constitutional requirements.”

But some lawmakers were not swayed by Cole’s explanation.

“Could you go to the FISA court and argue that you had a right to obtain an individual’s or every American’s tax return?” asked Rep. Blake Farenthold (R-Tex.). “Could you get at somebody’s permanent record from school?”

Cole began, “If it was relevant to the investigation, you could go to the FISA court and ask . . .

“Could you get somebody’s hotel records?” Farenthold interrupted “Could you get my VISA, MasterCard records? Can you get the GPS data from my phone, too? Do I have a reasonable expectation of privacy in anything but maybe a letter I hand-deliver to my wife” in a sensitive compartmented information facility?

In some of the cases, Cole answered that it would depend on whether it was relevant to a terrorism investigation.

“Snowden, I don’t like him at all,” said Rep. Ted Poe (R-Tex.), “but we would have never known what happened if he hadn’t told us.”

Rep. Bob Goodlatte (R-Va.), the chairman of the committee, said he was surprised that the programs had been kept secret for so long.

“Do you think a program of this magnitude gathering information involving a large number of people involved with telephone companies could be indefinitely kept secret from the American people?” Goodlatte asked.

“Well,” ODNI general counsel Robert S. Litt said with a slight smile, “we tried.”

Carol D. Leonnig and Craig Timberg contributed to this report.