Can you be taken to court? Yes.
Will you have the opportunity to tell the court what your ability to pay is? Yes.
First of all, if they did take you to court, you would have the ability to raise any defenses you might have, for example, that there was a failure of consideration, i.e. they did little or nothing for you, or that the charge is not reasonable or necessary. If they do get a judgment against you, then, under the NH court rules, they have to pursue a 'motion for periodic payments'. What that means is that they have to bring you into court and you will have to fill out an affidavit, under oath, telling the court about your financial status: what you earn, how much you have in the bank, what your assets are, how much you pay in bills every month, and all the rest.
I represented a company that had one of their bills stiffed by another company in a county next to yours. We got a court judgment in amount close to $50,000. However, after we brought the debtor in through this process we got an order of payment for $150.00 per month.
I represent some medical providers, so I have some sympathy for the urologists here. But, at the same time they are being overly heavy handed and they should be accepting your offer for payment of something/anything.
If your current monthly income is below the state median, and if all of your assets are exempt, you could file a chapter 7 and have the debt dischargede entirely. They SHOULD know this. It is of some leverage to you.