Rand Paul: NSA can't be saved by oversight The libertarian-leaning Republican said some of the programs "fundamentally" unconstitutional

Sen. Rand Paul, R-KY., known for taking a strong libertarian stance on privacy issues said Sunday that much of the NSA's surveillance program was "unconstitutional" and beyond saving with the addition of extra congressional oversight.

Paul, appearing on "Fox News Sunday," nonetheless called for a congressional hearing to address the agency's surveillance dragnet, which has recently been revealed to hoard information an almost every online and phone communication within and going out of the U.S., including the targeting of U.S. citizens' communications.

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"You know, I think it would be better with more oversight, but there are some things they are doing that I fundamentally think are unconstitutional," Paul said, noting: "Our founding fathers, when they wrote the Fourth Amendment, said a single warrant goes toward a specific individual and what you want to look for. ... The constitution doesn't allow for a single warrant to get a billion phone records. ... They basically, I believe, are looking at all of the cell phone calls in America every day."

"I think the president fundamentally missunderstands the constitutional separation of powers, because the checks and balances are supposed to come from independent branches of government," said the Kentucky Republican.

Meanwhile, on Friday, Democtratic Sens. Ron Wyden and Mark Udall -- both leading critics on the intelligence committee of the NSA dragnet -- stated that revelations about the agency's surveillance program were only "the tip of the iceberg." The senators said:

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We have previously said that the violations of these laws and rules were more serious than had been acknowledged, and we believe Americans should know that this confirmation is just the tip of a larger iceberg... We believe the public deserves to know more about the violations of the secret court orders that have authorized the bulk collection of Americans' phone and email records under the Patriot Act. ...The public should also be told more about why the Fisa court has said that the executive branch's implementation of section 702 of the Foreign Intelligence Surveillance Act has circumvented the spirit of the law, particularly since the executive branch has declined to address this concern.

Watch Paul's Sunday appearance below: