Just write a letter to the court letting them know why you want the hearing rescheduled, such as the need for additional time to prepare your defense. Usually, in credit card debt cases, things are pretty straight forward- you owe the money, you cannot make the payments, they take you to court to get a judgement. They will usually get the judgement. In most cases, your best bet is to file bankruptcy, which will discharge the debt. You may ask the court to reschedule because are in the process of finding a bankruptcy atty. Even if they get a judgement against you, you may file for bankruptcy later on and still get a discharge.
I would not spend the money on an attorney for the debt collection lawsuit, which will likely result in a judgement. Save your money for a bankruptcy atty, most will let you make payments toward the fee and will then file when you come up with the full fee.
Regardless of whom you contact, the attorney or credit card company, their only objective will be to get money from you.
Also, you have to be careful about reviving the debt. I am a PA attorney and not fully aware of the breach of contract statute of limitations in your state. However, if the statute of limitations is 4 years and you breached the agreement more than 4 years ago, then you can raise a defense to their action in court (basically the date of breach was the last time you paid-first time you did not pay) If you offer to pay them any money, after the statute has expired, you are reviving the statute for another 4 years, or whatever limit applies in your state. Again, it is likely that your best option is to save any money you have towards filing bankruptcy, which will give you a fresh start.