Four senators have unveiled a measure to rein in the surveillance powers of the National Security Agency. The bill from Democratic Senators Ron Wyden, Mark Udall and Richard Blumenthal, as well as Republican Sen. Rand Paul, is the most sweeping congressional response to date since Edward Snowden exposed widespread NSA spying in June. At a news conference, Senator Wyden cited what he called “sea change” in public opinion as a result of Snowden’s leaks. Sen. Udall, meanwhile, said the measures in the Intelligence Oversight and Surveillance Reform Act would protect Americans from unjustified intrusion into their private lives, in part by ending the bulk collection of telephone records under Section 215 of the USA PATRIOT Act.

Sen. Mark Udall: “This package includes ending the bulk collection of millions of Americans’ phone records, prohibiting the backdoor searches of Americans’ communications, and making the Foreign Intelligence Surveillance Court more transparent and accountable. Under this bill, the federal government will still be able to get hold of terrorists’ and spies’ phone records, but only where the government can demonstrate a suspected link to terrorism or espionage. And although I strongly believe that some surveillance programs have made us safer, Americans with no link to terrorism or espionage should not have to worry that the NSA is vacuuming up their private information.”

Democratic Sen. Patrick Leahy is not one of the bill’s co-sponsors, but has backed calls for similar reforms. The Senate Intelligence Committee is set to address the proposed NSA reforms at a hearing today. On Wednesday, NSA chief, Gen. Keith Alexander, criticized the outcry over government surveillance, saying Snowden’s leaks had sparked what he called “sensationalized hype.”