How likely is it to work out a payment arrangement after being served a judgement from a credit card company?

What do you mean that you have been served a judgment? Is this something from an actual judicial judge or just from the credit card company?

From my experience with credit card companies, once it has reached the litigation stage, if you can pay-off the payments that you owe in arrears, they will usually drop the pending action in court.

Have you tried calling them?

This is from an Attorney's office, an affidavit of plaintiff's attorney in support of attorney's fees.

Did you go to court?

If there already exists a judgment, there most likely won't be any reduction of that amount for a payment plan.

When ever I have had to sue someone, and they ask for a payment plan, my response is usually along the lines of "we had a payment plan once, that is what got us here to begin with".

You could have tried to get a plan set up at the time of the hearing, and if you plan to set up a plan on an existing judgment I recommend that it be done through the court. You pay the court, they keep track of the payments and balance, and send the payment to the plaintiff.

Outside of any official payment plan, with the judgment, they can now garnish wages or levy bank accounts to collect the amount of the judgment.

It sounds like you have been served with a summons, not an actual judgement. So the time to negotiate is now, before they get the judgement. There are hundreds of similar threads here that tell you how to deal with the summons.