The TSA process isn't very long, but then it depends how quick your flight school is with the I20... then you have to make your appointment at the Embassy which can be a few weeks away. If you are flexible enough you can generally get a quicker appointment and processing at the Consulate in Belfast. The documentation states to allow 2 - 3 hours for the appointment, but at Belfast I was in and out in 40 minutes, and my passport arrived home the following morning!
I think the whole process for me took about 6 weeks, but I didn't take the first appointment I was offered so it could be done quicker.