You can run it without the TPS, but that's really just a band-aid, and your performance/fuel economy will probably suffer everywhere but at idle. Since it isn't drive-by-wire (in other words, there is a physical throttle cable between the gas pedal and the throttle body) the TPS is just there to help the computer fine-tune fuel and air based on what the other sensors on the car are reporting.
So- have you done the usual routine? Remove/clean IAC valve; remove/clean/screw down retainer ring in FIT valve; warm engine and disconnect IAC connector, set idle screw, then re-plug IAC connector; reset your ECU; checked your vacuum level, and the whole system thoroughly for vacuum leaks; sprayed carb cleaner around your IM gasket? How's your PCV valve? Have you checked your coolant level after bleeding the system? Both the IACV and the FITV use coolant temp as a reference to do their job; if the level is low or there are air pockets in the system, things can get screwy. Most idle issues with these motors are related to vacuum issues, including the IACV and FITV; most of the rest are from low coolant levels. Spend a few hours under the hood and get it fixed right. Good luck with it.