President Barack Obama is being "disingenuous" when it comes to ending the NSA's bulk data collection program, which he could stop whenever he wants, Sen. Rand Paul, R-Ky., said Tuesday.

"Here's the thing about the president: He's disingenuous about this," Paul told "CBS This Morning." "The president started this program through executive order – he could end it anytime."

Key provisions in the laws the NSA uses to justify its phone-snooping program are set to expire on June 1, with the main debate centering on Section 215 of the Patriot Act.

President Obama has encouraged Congress to pass a measure called the USA Freedom Act, which would extend Patriot Act powers but rein in the NSA's ability to collect bulk records under Section 215. The House passed the measure with a 338-88 vote, but the Senate has been unable to muster enough support to move forward.

Senate Majority Leader Mitch McConnell, R-Ky., and other Republican leadership want to see the Section 215 renewed as it currently is, and have so far refused to support the USA Freedom Act, butting heads with supporters like President Obama and Paul. A third group of privacy advocates withdrew their support of the Freedom Act, saying it doesn't go far enough to protect Americans' privacy.

But Paul apparently doesn't believe Obama is willing to put his money where his mouth is.

"The Second Court of Appeals, the court that is right below the Supreme Court, has said that [bulk collection] is illegal. Why doesn't he stop it? What's he waiting for?" Paul said. "He [says], 'Oh, Congress can stop it.' He started it on his own. He should stop it, and I've asked the president repeatedly, 'Stop the program.'"

As for his reportedly strained relationship with McConnell, his main opposition in the Patriot Act debate, Paul says the two "are friends and we get along fine."

"We both keep it very civil. I have not had any harsh words with him or him with me, and I'm still hoping that we can find an arrangement that ends bulk collection. And if they were able to defeat me and reauthorize it, that may well occur, but it'll only happen if they let me have a vote on ending bulk collection," he told CBS.

"What I'm looking for right now is to see if the other side will negotiate. All I asked for was two amendments at a simple majority vote, so I'm not being unreasonable," Paul stated. "I would like to have a vote on ending bulk collection. I think we can win that vote."

Paul continued: "Our Founding Fathers thought it was very important that warrants have an individual's name on it – that you couldn't have a warrant that said Verizon on it and collect all the records of all the people in America through one single warrant," Paul said. "So I think I'm right in line with what the founders would've fought for. I'm proud of the fight."