I got my OR license through license transfer last summer. I started the process in mid-April, I took the MPJE in late May, I passed early June, and got my license July 3. I kind of took my time because getting it after July 1st let me be exempt from CE's from the first renewal. I probably could have gotten my license way earlier if I tried, Oregon is pretty easy.
ETA: Since the next poster talked about ATT time, I got mine the day after I applied for it. Very fast.