No, boys, the problem here is in the fuel pump. The single most comon failure in these pumps, because of their design, is lost spring tension in the flapper valve that is supposed to hold the fuel in the fuel line when the engine is stopped. The heat causes the cheap springs to die young, letting the fuel drain back into the area below the fuel pump while the engine is off. Very, very common, ESPECIALLY with the 'economy' pumps you can get at the cheap parts stores.
I have gone thru 3 pumps in 80,000 miles, all 3 with this exact failure. It always is fixed by replacing the pump. To learn more, take your old pump apart and you will immediately understand the problem. Partly, it's caused by the fact that this pump is mounted upside-down as compared to 'normal' orientation for these valves: originally the FoMoCo pumps had real springs and check valves inside, which today are just little stamped-spring steel pieces.
A true 'fix' is to convert everything to an electric pump, like an Accel or Holley. It's a pain, but lasts forever, and is my next plan of attack, since my mechanical now acts just like this again - this will be #4 pump in 84,000 miles. I can't start in the mornings without LOTS of cranking, a little bit of cranking at lunchtime, and immediate startup within 2 hours of the last run. As soon as I replace the pump, this will go away.
To check your car: when cold, pull off the fuel line at the carb. Disconnect your ignition coil. Put the end of the fuel line in a can, then have a friend turn the engine over by starter and see how long it takes to get fuel pumping into the can. If it takes more than 1-2 seconds, the pump is dying - or dead.
