Your wife's decision to stop paying at least part of her monthly minimum credit card payment will affect you, but probably not in the ways you might think.
First, the immediate impact on your personal credit score depends on whether your wife has listed you as an authorized user on any of her accounts. Some couples use this trick to kickstart a spouse's credit history, even though an authorized user doesn't actually have credit of their own to utilize. In some credit scoring models, showing up as an authorized user for a long-held account can make your own credit history seem longer, boosting your score. However, when your spouse's creditor starts reporting those accounts as delinquent, you can request that credit agencies strike those items from your record.
Second, if your wife racked up that debt before your marriage, you're under no legal obligation to repay it if she can't. Unless you live in a handful of states bound by community property rules, you're not even liable for that debt if she opened accounts after your wedding date. In most cases, if you never signed an agreement with a creditor, you don't owe that money. That said, expect some high-pressure phone calls from bill collectors who will try anything to collect that money from you. Say nothing to them over the phone, other than to request that they do not contact you by phone again.
Third, the effects of your wife's delinquency will start to show up on her credit report, which can hurt you if you're jointly shopping for good rates on mortgages, auto loans or insurance. All three of those products use credit scores to evaluate how much you'll pay in service fees and finance charges, meaning that you may have to go it alone (and report only your income) on future applications. In some states, employers even use credit reports during background checks, narrowing the field for potential jobs.
Finally, even though you might not be under a legal obligation to pay your wife's unsecured debt, it can weigh on your relationship if left unaddressed. Map out a plan to address the issue together, whether it means attending credit counseling, contacting her lender about a possible hardship payment program, or using a "debt snowball" style system to knock down the balance together. Avoid using a balance transfer offer to consolidate the debt unless you're willing to assume equal responsibility. Like these five common credit card mistakes, unresolved debt can find ways to undermine other parts of your marriage.