That's exactly what Dan Ciruli claims he did this past year. His resolution for last year was to start with a push up on 1st Jan and keep adding one every day ending with 356 the last day of the year.
Reminds me of a story of a young man who could lift a bull, the story goes the young man started lifting the bull when it was just a little calf. He did so every day and as over the years as the calf grew and turned into a bull the young man could still lift him.
I am not sure if this legend is true. I do find Dan's achievement inspiring.