Engine dies when I step on the gas

Here are some possibilities; start at the top, and work down

1) closed bowl-vent
2) stale gas; all the VOCs have evaporated, and the thick-chit won't light off. On a hot day, or after the engine is up to temp and shut off; the gas in the vented bowl will be stale in just hours.
3) low fuel level in the bowl
4) varnished slow-jet or passages
5) throttle is too far closed and the Transfers cannot respond fast enough
6) Cold intake manifold
7) loss of timing with loss of vacuum, or failure of the advance system
8) lazy accelerator pump.
9) bad coil.

Notice I put the A-pump near the bottom. This is because from idle to off-idle, as you described it, that pump is NOT the main player. The main players on a clean carb,are;
1) the freshness of the fuel
2) the fuel level, and
3) the transfer slots willingness to respond.
4) the entire fuel/air charge ALL making it into the cylinder, not puddling in the plenum or sticking to the cold runners.

Notice I didn't mention the power-valve/ metering rods either. They don't come on line until much later.

Happy Hot-Rodding

BTW, if the fuel is fresh, and the fuel level is correct, then it will run for a very long time; perhaps more than a minute, at idle; edit; with the fuel line disconnected or pinched. I forgot that part,lol.