"They say that everything is bigger in Texas, and apparently that includes credit card debt burden," said Matt Schulz, senior industry analyst for CreditCards.com.

The report assumed that borrowers would pay off 15 percent of their balances each month—a benchmark used by credit card debt counselors. Even with that steep payment, it would take a San Antonio resident with average debt and income 16 months to pay off his or her balance.

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Overall, the average balance doesn't differ much between cities—there is only about a $900 gap between the most indebted and least indebted metros. But median earnings vary by $18,000. So on average, citizens in all cities take on about the same amount of debt, but some have to pay it off over a longer period.

Over time, the average San Antonio debt will accrue nearly $450 in interest even if it is paid off at that optimistic 15 percent timeline. The average card holder in San Francisco will pay only $234 in interest and pay off his or her debt in nine months.

"Job No. 1 for anybody with a credit card is to pay that balance off at the end of every month, but if you can't do that you've got to make sure you're paying the minimum," said Schulz. "Otherwise the debt can get out of control in a hurry."

Schulz said he isn't sure why cities in Texas have higher debt burdens, but he noted that San Antonio has a large military presence. Service members are more likely to carry balances on their credit cards and have higher monthly debt expenses, he said. San Diego, another major military city, also came in high on the list of debt-burdened cities.

"If it was easy to boost our incomes in a big way we'd all be doing it, but there are lots of little things you can do to help knock down debt," said Schulz, including transferring balances to a card with a lower rate or simply calling the bank and asking for a reduced rate. "People might be surprised about how often that works."