What would you do?

I'm not working right now as I'm still on maternity leave with my 6 week old daughter. My husband has a good job and we've talked about me quitting mine and staying home with the baby for now. The issue is we have a lot of bills that have crept up on us over time...we could wipe out a lot of those bills as we have money in our savings but my husband doesn't want to do that he thinks we should save the money since I'm not working...I on the other hand would like to at least pay off a couple thousand dollars of our debt to ease my mind. His reasoning is when we get our taxes back in 6 months we can use that money to pay bills.... I'm not so sure though...
So my question is what would you do in my situation? Save the money up and not worry about the bills at this time and keep paying monthly payments OR try to pay them off now?