If I close a credit card with a balance, how much damage do I do to my credit?

I am having a trouble making my payments, I called to ask if they would lower my minimum payment. They declined. And the kicker ... they decreased my credit limit by $10,000! It's a Bank of America Card. I've never been late and a loyal customer for 10 years. Should I skip my payment... or close the account completely and take the hit. Your thoughts please.