Car will not stay running after started unless I.

Car will not stay running after started unless I stay in the throttle. When it does run, it runs very ruff. I drove it home and had my wife get out to see if she smelled like a rotten egg smell coming from the tailpipe. She said it did smell like that, and I also smelled it when I got out of the car. What could be wrong? I'm thinking the cat. Is bad, but don't want to spend that kind of money if it's something else.