You could hedge on that a little and to 100 every other day, allowing your body 48 hours to recover and rebuild tissue. Maybe 100 pushups on day one, then 100 situps (or other exercise) on the next day, alternating between the two. I would think that all 100 weren't in one set, that it's five sets of 20 or four sets of 25 or ten sets of 10 or something. Few people could ever do 100 consecutive pushups in good form - that would be equivilent to a sub 4 minute mile or other world record level event.
The reason I suggest that is because most people need 48+ hours recovery time when doing strength exercises, and pushups are much more a strength exercise than they are cardio.
When I was in basic training for the Army, I actually could do more pushups during the first week that I could when I finished basic training. Doing pushups became a little painful - because I wasn't allowed enough recovery time. And I wasn't the only person who noticed this. Weakarse people who couldn't hardly do any pushups increased, but people who were strong to begin with and who could far exceed the minimum standard before they even started basic often declined. About the only time that pushups didn't cause me some pain was on Mondays, that's because Sunday was a "day of rest" so we did situps instead of pushups. The military does a lot of stupid stuff that actually harms training more than it helps, but that's the guberment for ya.
This is a little off topic, but the guy who was my battery leader in basic was really short and stout, huge pecs like a bodybuilder. When he lead pushups, he spread his hands really wide apart so that his chest was only three or four inches above the floor, but with my bird chest and monkey arms my chest was closer to two feet above the floor, so he could do five pushups with less energy expenditure and in less time that I could do one. He did pushups as fast as he could count, less than a second each. I kept explaining to him that not many people could do pushups that fast, I explained why, but he always insisted on doing them super fast. By the time he had finished his twenty, I was on maybe number four or five.
There's also a video on youtube of an asian girl at a bench press competition. She was really short, got a really wide grip on the bar, arched her back like a gymnast so that once it was unracked it was only an inch above her chest. then all she had to do was to basically inhale while allowing her shoulders to drop a tad, and this brought the bar down to her chest (and her chest up to the bar). Then she exhailed and pushed her shoulders up a little, which put her back into her fully extended position. I think she benched something like three or four hundred lbs like this, and that technique apparently didn't violate any rules so she won and set a record - without her elbows ever having to bend. That ain't a bench press, that's more like a hold and twitch or something.
