Check the engine oil level first to ensure it is correct. If the oil level is correct it is likely to be the oil pressure switch that is faulty but the oil pressure should be verified using an il pressure gauge. The oil pressure on your engine should be 5 psi at idle and 30 to 80 at 3000 rpm
Dodge have a bulletin regarding this problem
This bulletin involves adding a terminal/wire/vent to the oil pressure switch connector.
THIS BULLETIN APPLIES TO VEHICLES EQUIPPED WITH A 2.7L ENGINE.
With a hot engine the oil pressure light may be on or flicker on at idle.
Verify engine oil pressure. If engine oil pressure is within specification perform the Repair Procedure.
Qty Part No. Description
1 05017800AA Wire Terminal/Vent
Remove engine oil pressure switch connector from switch.
Remove sealing dart from the empty cavity at the rear of the connector.
Pull terminal locking ring outward from front (switch) side of connector to gain access to terminal locking tabs.
Install wire terminal/vent, p/n 05017800AA, in place of the removed sealing dart. Slide locking ring back into place.
Attach the connector back on the oil pressure switch.
I acctually have the same problem with my cavilier. Originally when I took it in my they said my oil switch was leaking and replaced it and yet I still have low oil pressure when Idleing. I don't have alot of money and have spent over $400 to put in the switch and run all these test and still they don't know wht is wrong. If you have any other ideas on what it could be please email me at firstname.lastname@example.org. Thanks in advance