I have the same issue. Won't run or runs poorly with lots (whole lots) of white smoke. I had notice a little (very little) white smoke when my wife accelarated for a few weeks. My daughter left the lights on and ruined the already weak battery. The was running fine other than the little bit of white smoke when accelerating. It sat for a few days until I could get a new battery. Put the new battery in and it acted like it did not want to turn over. After several tries it did turn over normally but did not start right up. When it did finally start it blew a hugh cloud of white smoke. Now it won't run but in spurts and blows smoke constantly.
Only other out of the ordinary item would be I tried to charge the battery several times and tried to start it but the battery did not appear to have enough charge. it's turn over a few times then quit.
Check the oil for gas like morgan mentioned and if it has gas in it change the oil and take the carb apart and clean it,. Check and adjust the valves. Do a compression test and let us know what you find.