Usually at least 6 months.
Theoretically, the day you fall behind on a payment, they can file a lawsuit against you for breaching the contract, or cardmember agreement. However, this is a tiny breach of contract, not material, and they never do.
What generally happens is this:
1. the week after you miss your first payment —– your phone starts ringing
2. three months after you’ve stopped paying — phone still ringing and you get a letter that the account has been turned over to collections
3. six months after you’ve stopped paying — you get contacted and/or sued by a collection law firm.
4. seven months after you’ve stopped paying — if you haven’t responded to the suit with an answer, they’ll have a judgment.
What this means is that you generally can expect a lot of phone calls and nasty letters for the first six months or so, but that’s it. Your credit will take a hit for those late payments, but they cannot garnish you yet.
Even when they sue you, you have another month until they get a judgment.
This doesn’t mean that they can’t sue you more quickly. This also doesn’t mean that they may decide to drag this thing out for 8 or 9 months before they file a lawsuit. Simply put, you have some time to prepare your bankruptcy petition after you stop paying on that credit card.