Ames, Iowa (CNN)Texas Sen. Ted Cruz on Saturday urged Republicans to do something that he claimed had never been done before: nominate a Republican who supported Ronald Reagan for president in the 1980 primaries.

"Let me give you an amazing statistic," Cruz told a packed house at the Gateway Hotel in Ames, Iowa. "Do you know if you define as a Reaganite anyone who supported Ronald Reagan in the 1980 primary, do you know that the Republican Party has never once nominated a Reaganite to be president since 1984? Every single nominee since 1984 opposed Ronald Reagan in the 1980 primary. "

The pitch was clear: GOP voters now have the first chance since Ronald Reagan to nominate someone in the mold of Ronald Reagan. "I'm 45 years old," he said. "I have never once had the opportunity to go to a general election ballot and vote for a Reaganite on the ballot. We are inches away from doing that right here."

Is it really true that all of the other Republican nominees since Reagan's reelection contest in 1984 were not only Johnny-come-latelys to the Reagan Revolution, but opposed Reagan in those primaries?

"It's an outright lie," Arizona Sen. John McCain told CNN in a phone interview, adding that he firmly considers himself a Reaganite since his return from Vietnam. "Reagan had an emotional attachment to the (prisoners of war), so not only did we support him, we worshipped him."

The 2008 Republican nominee fondly remembered that Reagan held parties for the POWs upon their return to the U.S. from captivity in Vietnam, including festivities in Sacramento and San Francisco. "He wore a POW bracelet," McCain recalled. "It was very clear as early as 1973 that we appreciated his support and supported him -- all the POWs, including me."

McCain did not formally retire from the U.S. Navy until 1981, so he acknowledges he did not publicly and formally endorse any candidate for office until after then, because he was not permitted to do so under military regulations.

McCain "wasn't a public supporter" of Reagan, Cruz spokesman Jason Miller responded. "So the statement is accurate."

McCain ran for Congress in 1982 as an ardent supporter of Reagan and continued to work hard for the Reagan agenda once there.

"I was a foot soldier in the Reagan revolution," McCain told CNN. Even if his support wasn't public because of Navy regulations, "I supported him when he ran for president in 1976, and, of course, in 1980. To say otherwise is ludicrous."

Romney could not be reached for comment.

Other Republican nominees since 1980 include George H.W. Bush -- who challenged Reagan in those primaries -- and his son, George W. Bush, so they don't qualify as early Reagan supporters during that process. And 1996 Republican presidential nominee Senator Bob Dole also ran in the 1980 primaries, disqualifying him as well from this Cruz litmus test.

McCain and Cruz have clashed before. The Arizona senator once described Cruz and his allies as the Senate's "wacko birds," and earlier this month, he said questions about Cruz's eligibility to be president -- the Texan was born in Canada -- were "worth looking into."