I am thinking now that Nintendo's next home console will indeed show up at this year's E3. However, right now I am not going to believe any of the rumors about it (myself and many others learned this in the long run-up for the Wii), however, the rumor that it will release in late 2012 sounds believable and is in line with what I originally predicted. However, I will say that I did not expect for Nintendo to show off their next console at this year's E3.
Sakurai has said that he really wants to work on a HD console. Perhaps Iwata will now give him his chance.
Iwata: Good news, I am going to have your next project be a big budget HD title....
Sakurai:

Iwata: Its goings to be Smash Bros.
Sakurai:
Anyway, as to when development on Smash 4 is likely to begin. I think Iwata will likely pressure Sakurai to begin development as soon as his work is done on Kid Icarus Uprising (maybe even prior to it heading to market). Heck, there is the possibility that Iwata has relieved Sakurai from working on Uprising in order to get a teaser trailer for Smash 4 ready at this year's E3, though I consider it very unlikely.
I do very much expect that Smash 4 will be unveiled at next year's E3 (E3 2012). Its funny to think that we are now roughly a year away from seeing the next Smash Bros. I am quite excited. It looks like things will soon be like they were from 2006 to 2007, for better and worse. I am very interested to see what Nintendo has planned for their next home console.