If this is your first reaction, then you probably haven't stopped digging the money pit.
Not sure if this is the most helpful comment.
I'm in a kind of unusual financial situation. I've got the following debts, and could use some advice.
CC#1: 12.9% APR, $24000 balance
CC#2: 8.9% APR, $15000 balance
Car loan: 4.9% interest, $20000 balance
My mortgage is $2200/mo at 5.9%, and we're underwater on it.
My wife and I both work, kids are grown up and out of the house. Her paycheck covers all expenses except for the above, and I'm bringing in $5600/mo after taxes. We've got a $2K emergency fund, depleted heavily (and CC balances increased to near-max) over the last 2-3 years after a variety of home and car repairs. But now it looks like everything is stable, we're sticking to a not-particularly-stringent budget (consisting of "luxuries come out of her paycheck, no credit use allowed") and over the past two months I've already been able to knock down CC#2 by $5K and anticipate zeroing it out by January while making the CC#1, car, and mortgage payments, and then should zero out CC#1 in another 12 months, and the car loan will be gone a few months after that.
While you may feel this is unusual you are not alone in the amount of debt or kind of debt listed. Good news is many people before you have climbed and clawed their way out. You are on the way in getting out by paying off your CC’s.
To get a clearer picture I would say we need more information:
What is your wife’s income?
Do you have any other savings or investments?
Do you have a written budget where you match your expenses to your income? Check out this thread
on reducing expenses.
What is the balance on your mortgage? Personally, I would say no to the added credit card. The temptation to spend more seems too great as evidence by the balances on your current cards.