Some studies suggest that true overtraining can occur in as few as 6 days. (I'm thinking of one in which subjects did 1RM efforts daily.) This is a little scary, as it appears to take eight or more weeks to rectify.
Typically, if one's recovery is poor for three days in-a-row (beyond just DOMS), he's in a stale state. Depression, lack of enthusiasm, weakness, infections, and still other symptoms can suggest excessive over-reaching. Nutrition is half of the picture but there's also hot/cold contrast showers, massage, power naps, meditation, tapering or removal of gym efforts for a few days, etc. Recovery efforts should equal training efforts on a one-to-one basis (think "accountant's balance sheet"), especially when aggressively increasing intensity x volume.