If it's been sitting for a period of time since it last ran (if it's not a daily driver) then I'd say that it's just the fuel draining back out of the fuel bowl from sitting. Whenever I start my running parts car (rarely, once every couple months) I always spray starting fluid down the carb and start it. It runs a few seconds on that, then dies, so I repeat the process until the car stays running, which means the fuel pump has caught up and refilled the fuel bowl appropriately. This avoids damaging cranking and cranking.
Now if this happens overnight, then you might want to troubleshoot further, as I wouldn't want to do my once in a while restart process every morning!
Kevin