The reason there are these rumors about Bill Clinton is that he is the last president we’ve had since Roosevelt who would have had a shot at a third term if it weren’t for that dang meddling 22nd Amendment. Truman left his second term deeply unpopular, Eisenhower had health problems, Kennedy was dead, Johnson didn’t run for re-election for his second full term, Nixon resigned in disgrace, Ford never won election even once, Jimmy “History’s greatest monster” Carter failed to win a second term, Reagan was old and sick after his second term, and Bush the Elder failed to win a second term. That leaves Clinton. Despite the tawdry impeachment scandal Clinton left office with his reputation still somewhat intact. If he had been eligible to run against Bush the Younger in 2000 he might very well have won a third term.
Even if Bush the Younger secretly dreams about repealing the 22nd Amendment to allow him to run for a third term, the Republican party will never allow it, since that would allow the dread spectre of Bill running again.