"This is not a small hiccup," Wyden told reporters at a Capitol Hill news conference.
Efforts to rein in the once-secret surveillance programs have attracted an unusual coalition of liberal Democrats and libertarian Republicans, pitting them against House and Senate leaders who have expressed strong support for the NSA programs.
The bipartisan group unveiled the bill on the eve of a Senate hearing with the nation's top intelligence officials, Director of National Intelligence James Clapper and Army Gen. Keith Alexander, the director of the NSA, in hopes of jump-starting the debate over the programs.
"Americans with no link to terrorism or espionage should not have to worry that the NSA is vacuuming up their private information," Udall said.
The bill would change current law to prohibit the bulk collect of Americans' phone records and their communications data. The government could still obtain records of anyone suspected of terrorism or espionage and of an individual in contact with a suspected terrorist or spy.
Paul said he didn't understand how a "warrant that has 10 million unnamed people, all customers of Verizon" is consistent with the Constitution.
The legislation also would establish an independent, constitutional advocate to argue against the government in the secret Foreign Surveillance Intelligence Court and require the attorney general to declassify court opinions that address significant interpretations of the Constitution or current law.
Blumenthal, who served as Connecticut's attorney general, said secret courts were one of the reasons the colonists rebelled against the British government.
President Barack Obama has said he might be open to setting up public advocates who could oppose government lawyers at Foreign Surveillance Intelligence Court proceedings. But the administration continues to argue that the NSA programs are crucial tools in combatting terrorism.
Prospects for the legislation in the remaining months of the year are unclear as leaders of the congressional intelligence committees are strong defenders of the programs. But the disclosures from documents leaked by Edward Snowden, a 29-year-old former systems analyst on contract to the NSA, have stirred concerns among Americans that their civil liberties are being violated.
Wyden said that fact was underscored when he was asked about the secret court at the barber shop.