I know I already posted... but let me give you some actual numbers/stats from previous hunts.
In 2010, I hunted 9 days before taking a young bull. I never had a bull to respond to cow calls until the evening before my kill. They would occasionally answer a bugle (location bugle) but that was it. The evening before I took my bull two of us teamed up and called in two bulls from opposite directions, but it got dark on us.
The next evening I called two different bulls in to within 30 yards and killed my bull at 23 yards. The next morning my buddy called one in, but didn't get a shot.
I had hunted off and on all season... and took my bull on the 14th of September. It just wasn't good until about that time.
I didn't get to elk hunt in 2011 due to a ruptured disc in my low back. Last fall I was on the mountain before season came in and hunted everyday. I called in cows and one calf, but didn't have any luck with bulls until the 12th of September. Between the 12th and the 16th I called in 6 bulls (one was missed by my son, another was 15 yards from him but he couldn't get the shot, and I passed one at 15 yards because of a branch in the way).
When I left on the 16th... the bulls were REALLY vocal. That morning I called in two different bulls and they both got wind of me before I had a shot opportunity. I was hunting around 10,500'.
My experience has been that you may chance into one earlier... especially a cow or calf... but if you want the best action, and the best opportunity to take an elk, especially a bull... choose the time period that ferretWYO suggested.
I know there are many factors... ML's, other pressure, location, weather, etc. I will be on the mountain by the 8th of September and prepared to hunt as long as it takes.
Good luck... and let us know how it goes!