This was a strange one, wife and I were returning from a trip. I've flown lots of times, and flown on 737 series plenty of times. Pushed back from the gate, the ventilation quieted down, the rumble from the engine starting began, but we happened to be sitting on the side that was starting and saw great plumes of white smoke coming from the #2 engine for several seconds. Then we hear the rumbling slowing down and getting quiet again, clearly the engine was having some kind of problem. The plane had just landed and offloaded before we boarded, so it wasn't like it was a cold engine, and it was plenty warm outside. So we sat for a minute, and the captain got on the intercom and announced they were having trouble getting the #2 engine started. Well, that's comforting. A minute or so later, they tried again, and it started normally without the smokescreen. They started #1 after we had taxied a bit. Any idea what happened? Wife and I were fully expecting we'd be pulling back into the gate and boarding a different plane. I've just never seen smoke like that from a 737 engine, nor experienced a "no start". Usually just a puff when it ignites, and that's it.