Could be a plugged up fuel filter which is in the carburetor inlet.
Could be a stuck float valve, but not likely.
If fuel pressure is not up to specs, the fuel will not go past the fuel filter. Most later GM fuel filters have a spring loaded valve in the filter inlet and it takes pretty good pressure to open it.
After you check the points davidpozzi suggested, you might take a pipe cleaner and stick it down the fuel bowl vent tube to see if its filling up with gas.
If it is, then maybe a carb cleaning would be forthcoming. Remove the carb from the engine, tear it apart and clean all those nooks and passageways with aerosol carb cleaner. Assemble it back together and start the car and readjust the carb.
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