Not sure if this is related but Im having a similar issue with my 2003 People. Basically, anytime it's humid or after it rains, it either takes about 30 minutes to get going or cant get it going at all. Often it will start up right away but will idle out after about 10 seconds. What I noticed it that if I try starting it a few times, about 30 minutes before I need to leave, it will work....usually.
Recently I took it in for a tune up and had them clean the carburetor, thinking that would solve the issue. Granted, it now runs a lot better after having it serviced but Im still having rainy day issues. I keep it covered at night in a garage but it still gets a bit wet because there is a deck above my garage, therefore not completely covered from the elements.
Does anyone have any suggestions for this?