Rubio himself is "bullish" on his odds of winning the critical primary, despite some advisers who are less hopeful and believe a loss there would damage him politically in both the short- and long-term.

Publicly, the campaign is maintaining they are still a contender in this race, touting a Sunday win in Puerto Rico's primary that delivered Rubio 23 delegates. But privately, the campaign is having a debate about whether he should remain in the mix -- even for his home state of Florida's primary.

"He doesn't want to get killed in his home state," one source familiar with the discussions said, noting "a poor showing would be a risk and hurt his political future."

Alex Conant, Rubio's communication director, said the report of such an internal debate is "100% false."

"That is fiction," he told CNN's Wolf Blitzer on "The Situation Room."

"I was sitting in a senior staff meeting planning out next week's schedule when I saw this report suddenly air and I came racing across town to correct it," he added.