'83 Tercel Engine Dies After Start

I'm having a very odd problem with my car. Recently I was driving it and the engine just died on me. I started it back up, it stayed on for 5-10 seconds, and died again. I tried this a number of times, and finally to get home I had to start it and keep pumping the gas pedal just so the engine would stay on.

Any ideas as to what broke? I don't have fuel injection, and I don't think it's the electrical system because it started just fine and all the lights and the radio keep working.