You'd need to show your casefile to a family law attorney, including the judgment in question. My gut is telling me you're on the hook (Insofar that you can likely discharge YOUR attorney's fees, but not your ex's in many situations), but the devil is in the details because context/wording is everything.
These attorney fees have been generally held to be in the nature of support and are not discharged in a chapter 7.
Even though possibly not dischargeable, as the other attorneys have stated, your question also raises concerns about wage garnishment. If your employer is served with a garnishment order, you will have an oportunity to claim some, if not all, of your wages as exempt from garnishment. You should plan ahead for that possibilty and meet with a local bankruptcy atty (even if you're not going to file BK), to review the exemptions that may be available to you. Probably won't make the judgment go away, but could at least protect your wages for now.
Generally speaking, but not always, attorneys fees for your former spouse are not dischargeable in a Chapter 7 bankruptcy as they are found to be in the nature of support. What may be the right answer here is a Chapter 13 bankruptcy, wherein you could repay the debt over a five year period at a monthly payment that fits within your budget. So long as the plan presented is reasonable, it is unlikely that your ex or her attorneys would be able to successfully object to such a plan. It would be a tight budget, but it could be feasible.
Divorce Dividing debts in a divorce Divorce and bankruptcy Bankruptcy Chapter 7 bankruptcy Bankruptcy petition Bankruptcy documents Chapter 13 bankruptcy Credit Debt Wage garnishment Bankruptcy and debt Chapter 13 bankruptcy reorganization plan Criminal fines Lawsuits and disputes Working with a lawyer Fees