Is there a way to hardwire a phone jack into a car stereo system's factory unit to hook up an mp3 player?

You need a FM modulator, is an adapter for adding extraaux lines to any headunit. Is connected through the antenna cable, it simply block the fm stations signals when the adapter is activated, and thenplays the external source. here's one: http://www.crutchfield.com/S-yZWWXJiGrjW/cgi-bin/ProdView.asp?search=fm+modulator&i=142FMMOD01

Very few factory stereo systems are capable of this. You could consider an FM Modulator. This unit plugs into the cigarette lighter and the headphone jack of the MP3 player. You simply tune your FM radio to the same frequency as the FM modulator. I have one and it works great. They are universal as it will work with any device with a standard headphone jack. There is no wiring involved. Simple to move to another vehicle if necessary. A quality unit can be purchased for about $40. Follow the link below for an example of one of these devices, but there are several manufacturers of these units. They can be purchased at several on line electronics outlets of you can usually find them in the electronics section of your favorite department store.

don't be so cheap and buy it and do it right.