The basic premise: what if Naruto, during the 1-month hiatus between the Chuunin Exam preliminaries and the final matches, ran into Tsunade instead of Jiraiya, and suckered her into training him, probably by winning some outlandish bet in typical Naruto fashion?
Some considerations to be made:
-This Naruto will need some serious power in order to survive the Valley of the End, since he'd be lacking the Rasengan. Between Tsunade coaching him and the fox, however, pure power is something he certainly won't lack.
-He'll probably suck at basic medical jutsu, but will likely be able to pick up advanced ones really fast, which could give him a huge edge... he seems to stink at the basics, but drink up advanced jutsu like water.
-The fight with Neji would probably be horribly one-sided, as I'm willing to bet any medic-nin with enough power can probably free up his own tenketsu with relative ease.
-He might learn to summon slugs... or maybe something totally new. Who knows? In any case, Tsunade's main point is that she's not just very strong, but has obscene amounts of chakra, if the Genesis Rebirth is any indication. So Naruto is, ironically enough, a better fit to her mold than Jiraiya.
-Would that cause Jiraiya to become Hokage, since Tsunade would be the one around, would likely refuse, and thus would be sent to pick up her reluctant teammate?
Practically everything from the Chuunin Exams onward would radically change if Tsunade replaced Jiraiya. The above are just some of teh numerous things that could change.
I myself want to use this idea in my fic 'Twisted Fates', but it's mostly a secondary plot. It could do well as a stand-alone idea as well, which is why I put it up here for all to see. Feel free to pick the ball up and run, after all, chances are my version will be different from yours...