McConnell pressuring Rubio to run again
© Greg Nash
"I and my colleagues have been trying to convince Sen. Marco Rubio to run again in Florida," McConnell told radio host Hugh Hewitt on Tuesday. 
"He had indicated he was not going to, but we’re all hoping that he’ll reconsider, because poll data indicates that he is the one who can win for us. He would not only save a terrific senator for the Senate, but help save the majority," he added.
Rubio pledged when he ran for president that he would vacate his Florida Senate seat. 
Unlike Sen. Rand PaulRandal (Rand) Howard PaulGOP leader blocks resolution backing intelligence community on Russia Rand Paul blocks Sanders's Russia resolution, calls it 'crazy hatred' against Trump McCain: Trump plays into 'Putin's hands' by attacking Montenegro, questioning NATO obligations MORE (R-Ky.), who simultaneously ran for president and for his Senate seat, Rubio has said he believes it's important that presidential candidates run for the highest office without a fallback plan.
But since his campaign for president ended after losing his home-state primary, Rubio has faced intensifying pressure to reconsider his decision to retire. He has until June 24 — Florida's filing deadline — to decide whether to run again. 
Rubio insisted in a Sunday interview on CNN's “State of the Union” that he's unlikely to reconsider his plans to leave the Senate, because a close friend of his, Lt. Gov. Carlos Lopez-Cantera, is in the race.
But McConnell said he's not giving up.
"We’re all lobbying hard for him to run again," McConnell told Hewitt.
"He’s been back in the Senate for six weeks. He’s, I believe, enjoying it, and being effective. Fortunately, Florida has a very late filing deadline. … So I haven’t given up hope,” McConnell added.
"He hasn’t said yes yet, but there are an awful lot of us who think that it would not only be good for him and for Florida, but good for the Senate if he ran again."
McConnell, who is fighting to preserve the GOP's Senate majority in a tough 2016 cycle, is not the only senior Republican lobbying Rubio to run.
Presumptive GOP presidential nominee Donald TrumpDonald John TrumpNFL freezes policy barring players from protesting during anthem McConnell spokesman on Putin visit: 'There is no invitation from Congress' Petition urges University of Virginia not to hire Marc Short MORE, who taunted Rubio throughout the presidential campaign as "little Marco" and a "lightweight,” has made nice with the Florida senator in the weeks following his withdrawal from the race.