How severe does the debt have to be for a credit card lawsuit to be filed?
Some debt buyers will file suit for as little as $800

Credit card companies often sell delinquent accounts for pennies on the dollar to other companies (known as “debt buyers”), which file lawsuits to collect. But some credit card companies don’t sell their accounts. Lawsuits by these companies are called “original issuer” lawsuits.
Can a credit card company sue a debtor rather than just sell the debt?
Yes, they can, and some do. In Chicago and Cook County, American Express, Discover, and Capital One sue in their own name and will do so for as little as $800. As soon as you miss a payment, a credit card company could file a lawsuit against you, but most credit card companies will try to collect for months or years before filing a lawsuit.
Is there any way to defend myself against a lawsuit from a credit card company?
There are procedures that the attorney general and Supreme Court have set up for filing affidavits, which put a duty on the credit card company to investigate the debt. If identify theft or an unauthorized individual used your credit card, then you could have a good defense to the lawsuit. With that said, claims that a significant other or cohabitating partner used the card without your knowledge probably wouldn’t be a strong defense.