Nope, if otherwise qualified, they are as eligible as anyone. IIRC, we have more than one Convicted Felon in Congress. Obama's congressman, and Black Panther Bobby Rush(D-Chicago) for example. Alcee Hastings(D-FL 23) for another.(Now that is Gerrymandered District if I ever saw one.) Although technically Hastings is a not a *convicted* felon, but, as a Carter appointed Federal judge, he was impeached by a Democrate House and convicted in the (Democrat) Senate for taking a $150K (1981 dollars) bribe from a racketeer.
Now a President could be impeached and convicted for committing a felony, if in their judgment it rose to the status of "high crime". Diddling the interns and lying under oath apparently does not, if the President In Question is a 'Rat that is.
Nope, if otherwise qualified, they are as eligible as anyone.
I stand corrected. Read that somwhere. .