Actually, that's a rather dangerous way to approach acclimatization. While sleeping, your body systems slow down and you're far more prone to acute mountain sickness. The two most recommended methods of acclimatization are to climb high in the daytime and sleep low at night, or to gain no more than 1,000 to 1,500 feet altitude (net) between sleeping places each night. You'd do well to sleep at Estes Park the first couple of nights, going higher in the daytime.
Try googling "high altitude acclimatization"--all the references will tell you the same thing!
Be sure to keep well hydrated, take it easy the first few days and know the symptoms of HAPE and HACE--the only cure is to descend as rapidly as possible.