I think it depends a lot on the keyword phrases you are targeting. From my own recent experiences I have seen a couple of months on a website targeting fairly competitive keywords and about a week on a site for a not very competitive keywords.
For the first of these this was how the timing looked like. At the end of October a major rework of an older site to make it more search engine friendly including rewrite of dynamic URLs to .html. See the position results on our keyword below. (We did sit back and wait and didn't do much else in the time these results were taken.)
29th. October at position 109
27th. November at position 145
27th. December at position 105
10th. January at position 101
7th. February at position 21
Today it's 37 so I had better get cracking again
For the second site we changed the keyword phrase we were targeting and had results very quickly.
Danny