This area of law turns on specific facts and applicable state law(s). 

It is almost impossible to give a single answer for what you may think is a simple question.  First, the law of the state where you live or lived may control.  Second, a prior marriage or debts taken out before the current marriage may affect the answer. 

With these warning here are some basics (but you MUST talk to an experience attorney):

• The fact that the widow may have used the card during the marriage does not necessarily make her liable for the debt.
• The debt may be charged against the community property of the spouses, but the creditor has a deadline to sue or file a claim in the decedent’s probate case.
•  If the debt was incurred by the deceased in an earlier marriage was in a community property state, such as Arizona, the ex-wife may be obligated to pay the debt.
  

• Arizona has a claims bar date of 2 years post-death to file a claim against the estate or sue for a debt accrued by a decedent during his lifetime (” statute of repose”).  A.R.S. § 14-3803(A)(1).
• Schilling v. Embree, 575 P.2d 1262 (Ariz. Ct. App. 1977)
• In Re Estate of Van Der Zee, 265 P.3d 439 (Ariz. Ct. App. 2011)

These are only two of hundreds of cases that may help with this question.