US Senator Rand Paul has filed a class-action lawsuit against the Obama administration and the National Security Agency seeking to halt the NSA's vast data-surveillance program.

Paul, a Kentucky Republican and toast of the tea party movement, promised a “historic” fight against the NSA when he announced the suit had been filed Wednesday at a press conference. He was joined by Ken Cuccinelli, Virginia's former attorney general, and Matt Kibbe, the president and CEO of the tea party-affiliated FreedomWorks. Bruce Fein, a Reagan administration attorney, is one of the lawyers on the case.

The suit challenges the constitutionality of the NSA program that collects metadata on US citizens' phone calls.

“There's a huge and growing swell of protest in this country of people who are outraged that their records are being taken without suspicion, without a judge's warrant, and without individualization,” Paul said.

“I'm not against the NSA, I'm not against spying, I'm not against looking at phone records,” he went on. “I just want you to go to a judge, have an individual's name and [get] a warrant. That's what the Fourth Amendment says.”

Paul began telling the press about the lawsuit weeks ago. This, along with a 13-hour filibuster on drone activity inside the US delivered in March 2013, has fueled expectations that Paul will be among the Republican presidential candidates in 2016.

“Today we ask the question for every phone user in America: can a single warrant allow the government to collect all your records, all the time?” Paul said in a statement Wednesday. “I don't think so.”

The Obama administration has consistently maintained the data collection program, first unveiled last year by NSA whistleblower Edward Snowden, is legal. The 15 judges on the Foreign Intelligence Surveillance Court have reauthorized the data collection program every 90 days since 2006. In 1979 the US Supreme Court ruled that metadata – including the time of a call, its duration, and numbers dialed – is not protected by the Fourth Amendment.

“We remain confident that the program is legal, as at least 15 judges have previously found,” Justice Department spokesman Peter Carr said Wednesday in response to Senator Paul's announcement.

In December federal Judge Richard Leon ruled that the surveillance program is likely unconstitutional, deeming the technology “almost Orwellian.”

“I cannot imagine a more 'indiscriminate' and 'arbitrary' invasion than this systematic and high-tech collection and retention of personal data on virtually every single citizen for purposes of querying and analyzing it without prior judicial approval,” Leon wrote. “Surely, such a program infringes on 'that degree of privacy' that the founders enshrined in the Fourth Amendment.”