I don't know what a reasonable number to expect to be able to do by the end of the month is, though--I've never tried this before.

I don't know if you have to set a specific number as a goal (O mod, is there an official ruling on this? *g*).

Maybe you could set a goal of having a push-ups session twice per week through the months (or three times per week, whatever works for your body in terms of recovery time). Then you could just see how far you get.