Like everything else it differs very much how long it takes from city to city. For me to get it took months, my wife calling several times. Others say it took them very short time.
I would check with the airline. Perhaps I went with an airline that did not have a problem, so I tell you it is okay. But the airline you use may see a problem.
Maybe it would be easier for you not to come in on a visa exemp, but get a tourist visa in your home country. When you can arrange a visa before you come, it is more relaxing to be here.