Unfortunately, offers of settlement are considered irrelevant in court. The theory is that, just because some offer was made, the entity making the offer is not obligated to keep the offer available.
While I understand your point completely, the judge simply cannot make them abide by the offer they extended. So, to answer your question, it is more likely that they would prevail and a judgment would be entered.
Having said that, I would encourage you to continue to act in a "professional/efficient manner". If you can contact the attorneys office and/or the credit card company and get this thing finalized, you can still obtain your goal, that being a negotiated settlement that does not include a judgment.
I regret that my answer is unfavorable, but please understand that it would be unfair to you (and unprofessional of me) to provide you with anything less than a truthful response. With that in mind, I hope that you found value in my answer.
Also, several customers have asked how they may direct a question to me in particular. If you specifically want me to assist you in your legal matter, just put "FOR JOSEPH" in the subject line and I will gladly pick up the question as soon as I am on-line.