If your organism regenerates fasterthan that, then you don't have to.
Daily breaks between trainings are our proposition for you because most people really need them to regenerate muscles. Breaks matter especially if you do more than 50 push ups.
However if you are young and fit and after finishing all sets for one day you don't fell tired the next day, you don't have to take daily breaks.
Reember though that traininng becomes more difficult as you move forward, your muscles will have more work to do. If in the future you do start feeling tired and sore - start making breaks again.
During breakes you can train other parts of your body.