Ordinarily, I would look toward a clogged carb jet, but that is ruled out if it does the same thing with a different carb. It could be a kink in the fuel line or a fuel pump issue. Before you shell out $100 for a new fuel pump, check for a possible air leak at the connections upstream of the pump. Check the filter/separator too - the fuel pump will suck air before it sucks gas, and a small air leak upstream can cause the problem you are experiencing.
If you find everything is tight and there is no chance for a leak, you are likely looking a a new fuel pump.