Will not start without a prime

I have a 1997 Z-71 with a 5.7 throttle body. All original under the hood with 245,000 plus mileage. I used to be able to just tap the key and it would start. Now it has gotten to the point where I have to pour gas down the carburetor body to get it started in the morning. I can turn the ignition repeatedly and hear the pump run. Sometimes doing that will get it to start. If not, a half cap of gas will get it to start. It will then stumble for a few seconds then smooth out and be fine. It almost seems like the fuel line is draining back into the tank and needs the vacuum of the engine to pull it through the line. I replaced the filter, and this helped for about two days. Is there a valve in the pump or tank outlet itself that went bad?