By Carlo Muñoz - 06/11/13 05:07 PM EDT
The effort has the backing of Senate Judiciary Committee Chairman Patrick Leahy (D-Vt.), according to a release from Wyden's office.
Sens. Dean Heller (R-Nev.), Mark Begich (D-Alaska), Al Franken (D-Minn.), Jon Tester (D-Mont.) and Mike Lee (R-Utah) have also signed on as co-sponsors to the proposed legislation.
"I think they are going to eventually turn us down," he added, regarding the White House's response to declassifying FISA court opinions.
"They are [just] going to say no," he added.
The bill comes after classified information on two domestic surveillance programs run by the National Security Agency (NSA) were leaked by Edward Snowden, a 29-year-old government contractor.
Details of the NSA programs were published in The Guardian and The Washington Post last week.
One program was designed to collect cellphone data from Verizon customers to track terror threats, and a second program, PRISM, collected data from tech companies on foreign Internet users.
President Obama and the heads of the Senate and House Intelligence committees have defended the programs as critical to national security, and said they did not violate the civil liberties of American citizens.
"I think there needs to be more transparency here, but I think we can achieve it without jeopardizing national security," said to Durbin.
A possible compromise to the Markey-Wyden bill, Durbin said, would be having more lawmakers outside the Armed Services and Intelligence panels briefed on programs similar to the NSA surveillance operations.
"I think that is a good option," Durbin said.
The White House said Congress had been briefed on the operations, but many lawmakers say they were unaware of the programs and are demanding more information.
"The reality is [the White House] has made some classified materials available ... [but] during the regular course of events, it is a very limited number of Senators and congressman who are regularly apprised of developments" on sensitive intelligence or national security operations, the majority whip said.
Durbin has repeatedly pressed for additional congressional oversight of intelligence and national security efforts, particularly those like the NSA programs disclosed last week.
"I have been offering these amendments for years ... and losing them, regularly," Durbin said.
"And the two areas I have been focusing on are the two areas that came out last week," he added, referring to the clandestine monitoring of phone and Internet traffic of U.S. citizens.
Those failed amendments, according to Durbin, would have "established a specific connection between information sought and suspicion of terrorism, rather than a more generalized collection, which is going on right now."