When I applied in '03, I submitted my AMCAS application on September 29th. My secondaries were in by mid November (except 1). I applied to 9 schools and got 6 interview offers. 3 acceptances.
Interestingly, the one school for which I did not submit a secondary contacted me in January and asked if I would submit...I emailed them back and said I would not be able to come up with the application fee by the deadline...they said no problem, send it when I can...that secondary was sent on Jan 20. THEN, the MD/PhD office from said school contacted me saying, "Oh! You're interested in MD/PhD? Fill out this additional application." I did, got interviewed in April, and was accepted about 10 days later. I am now a 4th year at this school.
...like everyone else, I was told repeatedly to apply early, but this just is not my style. I think simply meeting the deadlines will suffice if your application is strong. If you are applying MD/PhD, your app better be strong.
Good luck!