I would never intentionally damage my credit just to get out from under a $40-45K debt when thus far you've been able to keep up. I'm guessing the credit card debt is spread over multiple cards.
If you have multiple credit card balances (and assuming the interest rates on all of them are relatively the same) then I would suggest paying the minimum payment on them all EXCEPT the one with the smallest balance. Pay as much as you can on the card with the smallest balance. This will get rid of one of you payments as fast as possible. Then once that card has been payed off, begin paying as much as possible on the remaining card with the lowest balance... Repeat and rinse until they are all paid off.
You may "think" you want to screw up your credit for 5-7 years just to get out from under that debt, but I would recommend against it. Your credit rating is one of the most valuable assets you can have. Many employers now days require a good credit rating JUST to get hired. What if you were to get laid off next week? Your credit could mean the difference between you being able to get another job or remain in the unemployment lines.
Quote:
My monthly income is 4,600.
Mortgage payment is 2400
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I certainly hope the monthly income you stated is net (AFTER taxes) and not gross (BEFORE taxes). Generally speaking your house payment (principal, interest, insurance, and taxes together) should be roughly 29-35% of your total gross monthly income (BEFORE taxes).