Car hanging on start?

I have a 1993 Buick Century. Today I started having a little problem with it. Usually I just hear that little sputtering-start up noise as I'm turning the key. But today,when I went to start it, I hear that normal little sputtering-start up noise, it stops (goes silent, doesn't start) for a second or two, and then sputters back and starts. I haven't really had any problems with it before, and I'm wondering what could possibly be causing this?