Could FDR or JFK win today?

[Kaine for Senate '18]

I was watching an episode of House last night, and they were talking about a Senator who planned on running for President despite having epilepsy.  One of the doctors mentioned two of the greatest presidents, FDR and JFK, and said JFK was the unhealthiest man ever in the White House.  House then said that neither would win today.  This got me thinking: could either of these men win today?  For that matter, would they even get the nomination?  Back then, the media didn't pry into the lives of politicians as much, so they could get away with being crippled, and having every disease known to man.  I don't think they would evne get their party's nomination if they had the chance, because the voters would not pick someone as unhealthy as these men.  What do you think?