There are many variables concerning this issue that you may need to weigh for your practice. Our situation is somewhat different than Jon's.
In primary care we don't have high-dollar-value procedures. Additionally, the copay sometimes is over 50% of the total reimbursement. An insurance company may say the "negotiated rate" is $65, and the person has a $40 copay. So for us the copay is a big deal and I'll go after them. But worse is the patients that have deductibles and don't want to the deductible. So they come in with serious and/or multiple problems and its a 99214. And the EOB says "patient responsibility--deductible." And the patient now ignores the bills and phone calls. This is someone who just isn't going to pay the bill unless forced, and I don't have any high-value proceedure that I can get from them. So I send them to a collection agency.
This has resulted in some ill-will, but the ill-will is from deadbeats.
I believe keeping the credit cards on file will actually improve our relationship with our patients. Over the last few days, I have been telling patients that beginning Aug 1 we will require this. So far everyone has been understanding. I'm sure I will lose some patients over this. But I've been told by some patients that their previous doctors, or doctors of their friends and family members already do this.