I don't know if a month was pushing it.  Given how the Uchiha have a slight learning curve advantage, and also Sasuke was already fast to begin with.  He was able to keep up with Haku in the beginning once he got the sharingan.  Plus he was training with Kakashi under whatever training method they used.  Given, Kakashi put Naruto under a training method that lead him one of his strongest jutsu.  A month training under Kakashi and being an Uchiha, I don't think a month was too early.