How much do you pay towards your CC's each month? It is not ideal, but depending on the amount - you could skip paying them in order to keep your electricity on.
I mean, it is the 4 walls. If you can't have a necessary utility on in your home, you don't have the money to pay towards CC debt. Sad to say, but true.
Of course, that is going to create its own mess that you will have to figure out.
But seriously, how did you let your electric bill get past due by over $3k? That takes quite a while to add up.