First time starts then dies, second time starts and stays

I am wondering whether it is that the engine is cold that this is happening. A guy at the gas station told me it has to do with the fuel line, that the gas is somehow having a hard time getting up the line.

Definitely only happens once, the first time I start it when it is cold. After that, the second time, it starts and stays on.

Anybody have any insight to give me? I'd appreciate any help.