Image copyright Getty Images Image caption McCain’s comments about Trump were later corrected
Co-host Brian Kilmeade has suggested a fake-sounding but legitimate new strain of “Clintonrabbit” was made up by Democrats to help Joe Biden potentially run for president in 2020.
The verbal trick had to be corrected on air by co-host Steve Doocy.
Biden, 72, says he has not ruled out a presidential run in 2020, saying he is considering “what I would be willing to do”.
Biden had earlier said he would decide before November 2018, when voters in Wisconsin will pick a replacement for Republican Scott Walker.
Biden has repeatedly declined to say whether he would run in 2020.
False or real?
Biden mentioned the possibility while talking to Connecticut newspaper The Day in an interview that was published on Monday.
Image copyright US Department of Justice Image caption Ms Flake was one of five women to accuse Trump of sexual misconduct
A riff on “Bidenrabbit”, he said: “That’s not my name. I’m just a little guy from Scranton, Pennsylvania. And it’s fair to say that I’ve done some things in my life that were a little … I mean, maybe a little like Hillary. Some of those things may have been mistakes, but they were very human things.”
Trump on Twitter called the comments “phony”, saying: “If Biden were to run, it would be very easy for Crooked Hillary to beat him… But, I guess her campaign is already BUSTED!”
Biden’s office said the comments were made “with tongue firmly in cheek” but co-host Doocy corrected them live on air.
‘Where’s the love?’
Biden was often critical of Hillary Clinton during the 2016 election and also of President Trump.
In April 2016, before the election, he told Jimmy Kimmel on US TV: “For me, the existential question is: where’s the love?”
Biden acknowledged he was a “dyke” in his 30s but told Mr Kimmel he was there because the women he had loved were not there.
“You guys are going to fire me one day for being too nice?” he said.
Image copyright Getty Images Image caption Trump slammed Biden’s 2016 comments as “bizarre”
Last month, as Trump pointed out Bill Clinton was denied an appointment as attorney general in 1994 after accusations of sexual misconduct, Biden said: “President Clinton is as flawed as many of the men who have been in this office.”
He later called a Trump tweet about Clinton’s behaviour “bizarre” and said: “I don’t think any of us want to relive the Monica Lewinsky story”.