If I backed into a car but there was no visible damage, what is my liability?
I backed into a co-worker's SUV with my car and there was no visible damage when I told the owner. She told me not to worry and that we'd work it out. A month later she gives me an estimate of damage I don't think was there. Should I pay?
Under the law, if you were at fault in hitting her car--which you probably were, based on what you have written--you would be liable to pay for any property damage caused by you.
Not all damage is immediately obvious, of course--sometimes the damage, especially to frame, chasis, etc., is not visible, and is only detected after driving. On the other hand, sometimes people try to cheat you and have you pay for things which aren't your fault.
Again, legally, you are only liable for the damage you caused. Whether you should pay or not depends on how strongly you feel you did not cause this damage, how much she is asking for, your belief as to whether she would sue you if you do not pay voluntarily, how much you're willing to pay to avoid the risk of a lawsuit, etc.