92 S-10 Blazer stalling

My Blazer has been running for the last 2 years with no problem. A couple days ago I started it up and went 25 miles to work, as soon as I slowed down for a stop light, it stalled. It started right back up and went 4 blocks to the next light and stalled when I slowed down. It wouldn't start after that. After work, I turned the key and it started right up and went the 25 miles back home only to stall out the first time I had to stop. I left it on the side of the road for 2 hours, came back and it started and ran the rest of the way home. The truck will run as long as it doesn't idle down below 1200 RPM, lower than that and it dies and won't start. I can hear the fuel pump kick in but no fuel at the carburator. I tested this by starting it up in the driveway, It ran great until it warmed up, then the engine slowed and it stalled, with no fuel at the carb. Is there a sensor getting hot that will shut down the fuel injection? Or am I in need of another fuel pump?