When I'm doing push-ups to failure, most of them are relatively effortless, then I'll have 2-3 where I'm feeling the strain in my arms and they start feeling rubbery, and then I can squeeze out 1-2 more push-ups, but only by clenching the muscles of my torso, my buttocks, and my legs. I've tried experimenting with not doing that (and thereby doing a few less) and it seems like that's correlated with not feeling muscles soreness the next day (it's not 100%, but those 1-2 extra push-ups just seem to put me over the edge).
I know that muscles soreness can be sign of breaking them down to build them back up, and that the last few reps, when you initially think you can't do any more, are where you're really getting the benefit of the exercise because you're pushing your limits. But, such pain can also mean that you're doing something wrong, or pushing yourself into the area of damage. So, the long and the short of it, is tightening those muscles to squeeze out the last rep or two a bad thing?