I'd say most heroes in Marvel were Independent politically. Socially, Logan would be a Democrat, since most attacks on mutants seems to come from more of a God-fearing very super-v. But he'd draw the line at anything smacking of political correctness, or laws on social issues such as smoking and drinking.
Spider-Man, I can't see him having the time to sit down and think about any of this stuff. Granted, since today's Republican party is so far out of touch of anything, they've lost sight of what they were originally founded over, he's more of a Democrat due to lack of any other good choice. With views on personal responsibility, he'd be a great modern day Republican, but since he's Marvel's poster boy, I can't see him being anything other than a Democrat.
Now, what really bugged me about the Civil War being used as a metaphor for political parties is that I can't see Democrats with their gun laws trying to keep super-humans from registering. This is the party that wants a .22 hunting rifle license that takes a 30 days backround check, not being able to transport it in a car, and if you fire it for whatever reason they take it away. It's really a fight between two versions of the Republican party, the old style Captain America one, and the new stuff, led by "OMG-EVERYTHING-IS-SCARY-SO-LET-ME-LEAD-YOU-PEOPLE-OF-EARTH!" Tony Stark.