If you have been served with a lawsuit, you better respond by providing an answer to the complaint. You can try to contact the attorney who filed the lawsuit to negotiate, but it seems like it is too late. If you don't respond to the lawsuit the attorney could get a default judgment against you. I strongly recommend contacting a litigation attorney in your area.
You always have leverage if you are uncollectable. You should file an answer to the lawsuit so that it does not go into "default" which would allow Titan to get a judgment against you. The $20,000.00 probably represents the insured's (person who you hit) Uninsured Motorist Limits or the amount Titan paid its insured for his/her injury.
Your question does not indicate when you got served with the lawsuit; you may already be in default. If you are uncollectable, Titan, most likely, will negotiate and settle for something less than the full amount, but you need an attorney to do the negotiating. Hire one immediately; his/her services should cost you far less than you will owe Titan if you don't. A judgment will damage your credit. If you can't afford a lawyer, call the legal aid office nearest to your home and tell them your story. For all others reading this post; this can happen to you. Do not drive if you are not insured; it is a one-way ticket to potential financial ruin.