The Democrats rejected his application:

South Carolina Democrats squashed Stephen Colbert’s fanciful White House bid on Thursday. His campaign ended on the Republican side as well.
Colbert, who poses as a conservative talk-show host on the Comedy Central cable network, filed to get on the ballot as a Democratic candidate in his native South Carolina. His campaign paid a $2,500 filing fee just before the noon deadline, said state Democratic Party Chairwoman Carol Fowler.

They didn’t think he was a serious candidate (I wonder were they go that idea). He failed in his bid to run as a Republican because he didn’t make the filing deadline. Probably because the price to run as a Republican is so steep: $35,000! Sheesh! Republicans really are the party of the rich.
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