"No, I think we have a way that we could do this, but it's not a question of fighting the president," Leahy said on Fox. "The question is, what is Congress going to do on this? ... I just think that there should be an oversight.
"I mean, I was a prosecutor for eight years; I believe in going after the bad guys," Leahy said. "And I realize this is an entirely different level of the bad guys that I went after, but you still have to have some checks and balances, or you have a government that can run amok."
The chairman of the House Homeland Security Committee, Rep. Michael McCaul, said that Obama was moving in the right direction.
"I think what gave most Americans heartburn was that this data was being stored under the NSA and warehoused under the government," said McCaul, R-Texas.
But McCaul allowed, "I think it's very difficult to decide who has the capability to store and use this data."
Sen. Mark Udall, another critic of the NSA surveillance program, praised the president's ideas and said the limitations Obama proposed mean that "we won't collect every Americans' phone records almost every day."
Udall, D-Colo. and a member of the Senate Intelligence Committee, said Congress has a real motivation to make meaningful changes to the program because authority to conduct the spying under post-9/11 laws expires next year. "So we have real motivation to get it right and to work together," Udall said.
Feinstein and Rogers appeared on NBC's "Meet the Press." Rogers also appeared on CNN's "State of the Union" and CBS' "Face the Nation." McCaul appeared on ABC. Leahy appeared on "Fox News Sunday." Udall appeared on CBS.
- NORAD 'tracks' Santa's journey across globe
- Officer kills armed 18-year-old near Ferguson
- Women excised from public life, abused by IS
- Severe storms slam the South, killing at least 4
- Wal-Mart tests gift card exchange
- Sony broadly releases 'The Interview' in...
- Key developments in the case of slain NYPD...
- Denver shelters cite legal pot in homeless...
- Police boss: NYC cops 'quite simply,... 17
- NYPD: Cop ambush killer told passers-by... 15
- Going it alone, Obama rocked the boat... 13
- Key developments in the case of slain... 9
- Pope in blistering critique of Vatican... 8
- Officer kills armed 18-year-old near... 8
- Killings of 2 New York officers trigger... 6
- Senate, CIA agree torture program was... 6