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Sen. Dick Durbin (D-Ill.) on Sunday hailed the House effort to block the National Security Agency’s collection of phone data and said support was growing in both chambers for greater oversight.

“This was an amazing vote. We came within six votes of challenging an intelligence operation. That doesn't happen very often, hardly at all,” said Durbin on ABC’s “This Week.” “It's an indication of a healthy democracy where the oversight of Congress on even security issues is important.

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“The last time I called this same issue for a vote, an amendment I offered the Senate Judiciary Committee, Sen. Mike Lee, a Republican of Utah and I co-sponsored it, only one other senator joined us in that vote,” Durbin continued. “It's clear that the sentiment is growing for oversight. And I think that the efforts by Sens. [Ron] Wyden [D-Ore.] and Mark Udall [D-Colo.] as well as [Sen.] Jeff Merkley [D-Ore.] is going to increase that effort for oversight. That's a healthy thing.”

The House last week voted down an amendment to a Defense spending bill from Rep. Justin Amash (R-Mich.) which would have defunded the NSA's collection of phone metadata. Despite the strong opposition of the administration and intelligence leaders, the measure failed in a close 205-217 vote.

But the effort is likely to spur further challenges to the NSA.

Sen. Wyden said in an interview on C-SPAN that the vote had "accelerated" talks about NSA surveillance in the Senate.

"You are going to see a very strong and bipartisan effort in the Senate to pick up on the work of the House," Wyden promised.

Wyden and Udall are working on a bill which would amend the Patriot Act and prevent the NSA from collecting phone data on American citizens.

Durbin on Sunday suggested one reform could be the creation of a civil liberties advocate to speak for privacy issues before FISA courts.

“In this case, it's fixed in a way, it's loaded. There's only one case coming before the FISA, the government's case,” said Durbin. “Let's have an advocate for someone standing up for civil liberties to speak up about the privacy of Americans when they make each of these decisions.”

Sen. Saxby Chambliss (Ga.), the ranking Republican on the Senate Intelligence Committee, however, said that while he agreed with the need for proper oversight, lawmakers must be careful not to remove an important tool for counterterrorism.

“I agree with Dick that the right kind of oversight is absolutely necessary,” said Chambliss also on ABC. “And we have got oversight now of this program, both by the Department of Justice, by NSA, by the FISA court, by the intelligence committees, by the Judiciary Committee.”

"There is no other program in the intelligence community that has as much oversight as this one,” he added.

Chambliss, though, said he was open to “some changes to make things more transparent.”

“But we've also got a responsibility as policymakers to make sure that our intelligence community and our law enforcement community has the tools with which to provide the kind of protection that we've had since 9/11,” said Chambliss.