Smoke coming out of carb

I finally pulled the Duster out of storage yesterday. It's got a slant six with a Carter 2BBL. I had to remove the choke plate and tickle the throttle to get it to start, but otherwise it seemed fine.
After idling for about 10 minutes, I noticed some gray, wispy smoke coming out of the top of the carb. When I shut the engine off, a lot more smoke came out, almost like a small fire was just put out. I looked down the carb and didn't see anything wrong with it, so I'm guessing the problem is with the engine itself.
Before I do anything drastic, does anyone have suggestions as to what might have caused this?