Sounds like it could be the TPS or maybe the fuel system is leaking down while it sits...it's hard to diagnose when you can't see the thing let alone run checks on it. Search the board and maybe you'll find that someone has had the same problem and how they fixed it. Or maybe someone will chime in with more ideas...
Just a thought, but have you tried running a fuel system cleaner through it...possibly dirty injectors...I guess if that was the case it would run rough all the time tho...
2005 Liberty Limited 3.7
2005 Grand Cherokee Limited 4.7