Sell Car, Then Lease?

Young and dumb we financed a brand new 2012 Mazda 2. Payments are $270 a month and we have $3,400 left to pay, ending in about a year.

We also lease a car for $150 a month.

Since we bought the car we've become homeowners in an expensive part of town (schools!), had a kid, had a medical scare with the kid, incurred a few expensive but necessary home expenses - we haven't been great budgeters until recently. Needless to say, we are in credit card debt. We're working our way out and are looking for ways to save.

Fortunately we don't need two cars 99% of the time. We drive together to work and rarely have a need for two cars in general.

Best case scenario we sell the car for $5-6k and maybe lease a second car for much less than $270.

Does it make sense to sell the car so close to the end of paying off?