It sounds like you have Delayed Onset Muscle Soreness, or DOMS for short. This is perfectly normal if you are performing long sets of pushups with proper form. Proper form being that your torso is board straight from your head to your feet. DOMS is more prevalent when you drastically increase your efforts for any muscle group more than it is used to being stressed. In any given set, your abs are engaged the whole time to help remain that straight as a board form, while your arms and chest have small breaks as they are moving.
The good news is that as your body adapts to the new level of work (and rate of increase), the DOMS will go away. That said, some warning signs to watch out for are:
- Sharp, or intense pain while exercising either in the body of a muscle or at a joint.
- Dizziness, or near blackout feeling.
Sharp, intense pain is usually indicative of an injury. The most common form of injury on a program like this is tendinitis. Be sure to stretch and move your arms through their full range of motion when you are done.
Dizziness or that blackout feeling can be indicative of improper breathing or dehydration. If your plan is to do 100 pushups or more in one set, you will have to learn how to breath during the set. The program helps build up the reps you perform, so you will be able to figure that out. Dehydration will be the biggest risk--particularly if you train outdoors in extreme temperatures (either hot or cold). Be sure to drink plenty of water.