Can creditors come after me for debts my wife owes?

I am a lawyer in CT and practice in this area of the law.  Unless TX is considered a community property state, where the creditor may go after either spouse regardless of whose debt it is, then you should not have to worry about the debt in your wife's name.  in other words, the debt is governed by contract law.  you may not be held responsible for credit card debt if you did not agree to the terms and conditions of the contract.  I suggest that you hire a lawyer to find out if your state is a community property state to determine whether you are exposed.

There is a common misconception that there are "community debts" or "community liabilities."  The general rule in Texas is that liability follows only direct/indirect responsibility for debts and liabilities for one's spouse and children.

Direct responsibility occurs when a spouse signs an instrument or contract obligating himself or herself.  A common example would be an application for credit signed by both spouses.  Both spouses are responsible for the debt incurred. 

Indirect liability is based on agency principles and the doctrine of necessaries.  Under the Texas Family Code, a person is personally liable for the acts of the person's spouse only if: (1) the spouse acts as an agent for the person; or (2) the spouse incurs a debt for necessaries.  A spouse does not act as an agent for the other spouse solely because of the marriage relationship.  What is "necessary" varies from case to case, and is dependent upon one's station in life.  At a minimum, necessaries include food, clothing, shelter, and non-elective medical care.

You are not directly responsible for the debts ( because you did not sign for the credit cards), nor indirectly responsible sincenone of the debt seems to have been incurred for necessaries (you pay all of the household bills); it appears that you may bear no responsibility for your wife's debts.  You should, however, consult with an attorney in your area as well.