Car hesitation and stuttering..please help!!

My gf has a 2005 dodge neon with 50000 miles on it.. whenever she starts it up after it sits for awhile the car sputters and hesitates like it's going to die.. even after driving it for awhile and she comes to a stop at a light it sputters a bit like it's ready to die. Not a big deal until today we drove it up the street, parked it.. came out 10 minutes later and it started up but then as we were backing out of the parking spot it just died. Go to start it and it starts up fine and we drive off.. Any feedback is appreciated.. I dunno if it matters but she's had the oil changed about 2000 miles ago.. transmission flush also.. thats about it.

When was the last time it had a tune up? Spark plugs, air filter and so on?