"It's clear that the sentiment is growing for oversight," said Richard J. Durbin, D-Ill., the Senater's second-ranking Democrat.
The idea that the NSA is collecting the phone records of everyone "on the off chance" that someone may be a suspect at a later time "goes way too far," Durbin said on ABC's "This Week.".
The House last week came close to approving a measure to curtail the program in a vote that scrambled the usual political alliances.
Republican Reps. Mike Rogers of Michigan and Peter King of New York defended the program as a critical tool in the war on terrorism.
"Remember terrorists now use the same communication systems in America that we do," Rogers, chairman of the House Intelligence Committee, said on CBS's "Face the Nation."
King, appearing on CNN's "State of the Union," called it "absolutely disgraceful" that so many Republicans voted to defund the surveillance program, "which has done so much to protect our country."
"I mean, we are a party of national defense," King said.
Rogers said the program has been misunderstood. "There is no recording of phone calls. There's no dossiers," he said. "There's more information in a phone book than there is in this particular big pile of phone numbers."
Sen. Saxby Chambliss of Georgia, top Republican on the Senate Intelligence Committee, contended that the program is scrutinized.
"There is no other program in the intelligence community that has as much oversight as this one because people deserve to have their privacy protected," he said on ABC. But he acknowledged that some changes may be necessary "to make things more transparent."
Sen. Mark Udall, D-Colo., however, called the bulk collection of U.S. phone calls an invasion of privacy.
"The NSA is literally collecting every phone record of every American every day," he said on CBS. "We don't need to do this to fight an effective war against terrorism."
"The content of those phone calls is not available. But I think knowing when I call somebody, from where I call somebody, and for how long I call somebody is a violation of your privacy," he said.
"We're vacuuming up innocent Americans' phone records. Let's restrict that to terrorists or spies," he said.
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