When in the US some years ago, I bought the ticket at the gate and walked down the ramp to the plane as soon as I had been handed my boarding pass and receipt. As soon as I had sat down we pushed back.
If you want the detail I was trying to fly with a colleague from La Guardia to Indianapolis (sorry not so good on the codes) having not bothered going to Newark as someone had dug into the main power cable and much of the airport was blacked-out. We arrived at La Guardia to find our carefully arranged alternative flight cancelled. The alternative alternative left from the next terminal in 15 mins and went via Detroit (Northwest, you may have guessed). So, we ran over to the next terminal, went straight to the gate, slapped a credit card on the desk and said "Two for Indianapolis, please". The carry-ons we had were too much for the overheads as the flight had already boarded, so they had to be checked, but they made the connection and all was well in the end.
Of course, you wouldn't stand a chance now with security being what it is, but in those days, it really could be like jumping on a bus.