My wife and I had this exact thing happen. Not sure if this applies to your wife, but mine grew up in extreme poverty and had severe anxiety issues about not having enough money to eat. Even if that doesn't apply, her getting defensive shows she might has some easily resolvable issues with money barring anything like gambling or addiction. 

I think there are two issues: one issue is the debt and the other issue is her not putting extra on those cards. 

I approached it like this: Asked her to sit down to only look over the finances without talking about why things weren't getting paid, but I made it clear we needed to talk that through soon after. I went over the numbers with her, came up with a budget with her input, and we agreed to go over our finances once a month. I did my best to keep it light because I know my wife and I know she wouldn't consciously go "I could put extra to debt, or I could just not do it because lol"

The next day, we talked about why it happened. I told her I wasn't happy, but I wanted to solve things instead of complaining about her mistakes, and we talked it out. She had a hard time with money since she didn't have enough for food as a kid, which contributed, but the biggest factor was that she was totally overwhelmed handling our finances by herself on top of everything else in her life. She said one month we had an unexpected expense and she covered it with the extra debt payments, never readjusted the auto pay, and wound up with a lot of anxiety about it because she didn't know if she should keep making minimum payments in case something else came up, and felt so ashamed over not knowing what to do that she didn't want to bring it up. I handled our savings/investments, she said she realized how meaningless her concerns were when we went over our savings and investments the day before.

This all made me realize she wasn't the only one at fault and I told her so. We share responsibilities, share money, but I wasn't involved in bill payments and she wasn't involved in savings/investments. We agreed to each keep handling those things individually, but to go over everything once a month or as needed. Now, she feels comfortable asking questions and doesn't worry about having enough because she knows what we have squirrelled away. 

I'm sure people will tell you to leave her, but dude this is totally solvable with open communication as long as there's not something crazy going on. Just approach it as a problem for you both to solve and not one person's problem.

Also, put this off until after her birthday. I'm sure she's worrying about talking about it today, maybe try saying something like "we don't have to talk about money today, let's do that Friday. I'm sure it's overwhelming to handle it all on your own, so all I want to do is figure out how I can help and how we can make sure we're on the same page in the future. I love you"