I got a pretty good idea for a cooperative multiplayer game. By multiplayer, I mean people play on the same computer, just using different keys. Is this a bad idea because people aren't gonna be able to vote on the game unless they have someone else to play with?

For a GameJam its probably not a good idea. Most people will be playing solo so if the game requires more than 1 person or split attention it would probably detract from the experience. On the other hand if you dont care how you rank or how people vote and you want to use this as an opportunity to test out a proto-type, go for it.