The answer to this question is complicated. If you have signed a written agreement or as it is usually called, an authorization and assignment, then your failure to do so and your lawyer's failure to do so can get you both sued by the doctor. The best approach under these circumstanced is to negotiate with the doctor on a reduced payment.
If you haven't signed anything and the doctor isn't nipping at your heals (or his collection agency) then you have a decision to make. You can wait for the three year statute of limitations to expire in which case the doctor can sue but will get booted out of court for not filing in time. Or, you can contact the doctor's office and seek a reduction.
What if you submitted your health insurance? This too is complicated but typically health insurers have agreements with doctors to accept a certain amount of money for certain activities. For example, a doctor may perform an x-ray of your low back and the bill says $100.00. Blue Cross may have an agreement to pay them $33.00 for the x-ray. So what happens to the missing $67.00?
Nothing should happen to it. The doctor is a party to a contract with Blue Cross that stipulates that they get paid a certain amount and that is that. Talk to your lawyer if the doctor is trying to collect the remaining money,