Some of the most vocal critics of the National Security Agency in Congress believe they are being intentionally cut out of a looming debate on how to reform the agency's program that collects bulk telephone data.

The House parliamentarian on Wednesday gave primary jurisdiction of a newly introduced bill that would repurpose much of the NSA program to the chamber's Intelligence Committee instead of the Judiciary Committee, leaving members and aides of the latter group to cry foul play.

Matters involving the oversight of the intelligence community's broad legal authority have always fallen to the Judiciary Committee, a staffer said, adding that he could find no instance since the terrorist attacks of Sept. 11, 2001, that his committee did not get first claim on such legislation.

"Many of our members are pretty outraged," the staffer said. "They're trying to undermine this committee's clear jurisdiction, as the debate we're having is on civil liberties and constitutional rights." The maneuver, he said, puts NSA reform in "the hands of its biggest cheerleaders."

One of those outraged Judiciary members is Rep. Jerrold Nadler, who quickly issued a statement saying he was "deeply concerned that today, for what appears to be the first time ever, a FISA reform bill has been sent first to the House Intelligence Committee."

Nadler added: "The House Judiciary Committee must be the primary Committee at the center of this reform."

The bill in question was introduced on Tuesday by Reps. Mike Rogers, chair of the Intelligence Committee, and Dutch Ruppersberger, that panel's top Democrat. Both, especially Rogers, have been adamant defenders of NSA surveillance since Edward Snowden's leaks began last June.

(Related: Lawmakers, Obama Want to End NSA’s Bulk Data Collection)

But the two have changed their tune following the unveiling of their bill, which came on the heels of a New York Times report that President Obama was endorsing a proposal that would keep telephone data in the hands of phone companies and require court approval prior to every search of a targeted phone number.

The bill adheres closely to a set of reforms backed by Presdient Obama, but would allow the NSA to force companies to turn over particular records—orders the Foreign Intelligence Surveillance Court would review after the fact.

The coalescing around a general framework of reform—and Wednesday's procedural coup—does not bode well for the USA Freedom Act, which was introduced last year by Rep. Jim Sensenbrenner. The measure from the Wisconsin Republican and author of the post-9/11 Patriot Act, who sits on the Judiciary Committee and is a former chair of the panel, would require a stronger burden of proof for data searches and limit some of the NSA's other programs, including surveillance of overseas Internet traffic.

The Freedom Act, which has more than 140 cosponsors but has seen little progress lately, had been referred to Judiciary, leading staffers there to expect the same would be done for Rogers's FISA Transparency and Modernization Act. Now at least two Judiciary aides have expressed concern that the committee could be cut out of the review process entirely, as Rogers and Ruppersberger may attempt to bum-rush their bill to the House floor.

House Parliamentarian Tom Wickham and a representative for Majority Leader Eric Cantor did not respond to a request for comment. The House Intelligence Committee declined to comment on the record.