Another question I get here at Frugal Living is "Should I save money, or pay off bills first?"
If you ask that question in a room with ten frugal living and personal finance experts, you'll get fifteen answers. I'll throw mine into the ring:
It's never a good idea to put all of your money into one pot. If you're in debt, you need to get out as soon as possible, but if you have no savings, you need to get some started immediately.
Why not get the best of both? After your basic bills are paid, divide whatever money you have and put part of it toward paying down bills (pay extra) and put the rest into a savings account. You will eventually be in a position to handle any money emergency without worry.
The argument for starting a savings along with debt down payment goes like this: If you don't spend all your money paying down debt and something happens (your car needs repairs, you have unexpected medical expenses, etc), you can cover them with cash and not go deeper in debt.
All of this supposes that nothing is going to happen for awhile. If it does, be a little more frugal (or a lot more frugal if you need to) and pay as much in cash as you can.