When training to failure, how do the last reps feel?

Piggy backing off of this because it's somewhat related to my question: The past couple days I've just started doing a little workout plan where I do 200-300 Push ups a day, usually 20 or 25 at a time. Nearing the end of the 200, I'll start to get fatigued to the point where I'll go down and literally can't push myself back up. It won't even hurt or anything, feels nothing like a burnout from a rested condition, I just have to collapse because I'll sit there straining for 20+ seconds trying to go up but I can't muster any strength.

So the question is, am I doing anything wrong here? Should I be feeling burnout pain? What am I supposed to do if I get to 10 push ups and just go any further? Should I give myself more time between sets or is this kind of fatigue a desirable result?

/r/Fitness Thread