At least four different Senate committees have jurisdiction over the leaks by former NSA contractor Edward Snowden -- and now Sen. John McCain (R-Ariz.) wants to create one committee to rule them all.

McCain introduced legislation on Tuesday that would create a special new committee to investigate the NSA. He has been calling for the creation of such a committee since October, and the resolution is his first concrete step toward that goal.

"Now is the time for Congress to improve how it executes its constitutional oversight duties," McCain said in language accompanying the resolution. In the past he has been less diplomatic, stating that the Snowden leaks have revealed that existing House and Senate intelligence committees "haven't done their job."

Sen. Dianne Feinstein (D-Calif.), who chairs the Intelligence Committee, threw cold water on McCain's idea.

"There is no need for a select committee to review the Snowden leaks or NSA collection," Feinstein told HuffPost in a statement Wednesday. "The Senate Intelligence Committee has conducted and continues to conduct thorough oversight of all intelligence collection activities by the National Security Agency and other intelligence agencies."

Like the 1970s-era Church Committee, McCain's committee would be charged with investigating domestic NSA surveillance. But it would also have another mission unlikely to please Snowden supporters: McCain is calling on the committee to investigate the "grave damage" he says Snowden's leaks have caused.

Another major difference between the original Church Committee and McCain's proposal is that the latter would concentrate only the NSA. In the 1970s, investigators also looked at other agencies like the FBI and the CIA. The recent White House review panel likewise extended the scope of its report to intelligence activities beyond the NSA alone.

One member of the original Church Committee -- which revealed that, among other things, the NSA once collected copies of every telegram sent into and out of the U.S. -- has been skeptical of McCain's proposal in the past.

"It seems to me that Senator McCain is in a way scoring political points here," former U.S. Sen. Gary Hart (D-Colo.) told HuffPost back in November.

Snowden supporters are taking a cautious look at McCain's proposal. Trevor Timm, executive director of the Freedom of the Press Foundation, has in the past called for a modern-day version of the Church Committee.

"Any proposals that would look to further criminalize whistleblowers or reporting would be very worrying," he told HuffPost in an email. "The panel should stick to what is concerning so many Americans: the culture of misinformation at the NSA and how much mass surveillance is being conducted on ordinary citizens."