I don't think there is any mechanism in place to really have a "do over" and so the Democrats basically get away with the whole thing -- the ship of state sails on without a real course correction. Obama would just be shuffled off stage, race riots would break out, and Joe Biden and Nancy Pelosi would continue to implement fascism. Probably declare martial law and solidify the coup.
Indeed. The Constitution allows for the removal and succession of a POTUS that's unfit or incapable; however, it does not anticipate the assumption of the office by one unqualified to hold it.
I personally think the best solution is set forth in Section 4 of the 25th Amendment. Biden, with a majority of the cabinet, could legitimately assume the powers of the presidency (note that right now, it is uncertain if anybody actually holds those powers, which was at the heart of MAJ Cook's case). Once this is done, Congress can hold O's resumption of the office in abeyance until he satisfactorily demonstrates he's eligible for the office. Until he does so, Congress can indefinately extend Biden's presidential authority right up until the 2012 elections. I think this would be an even better solution than impeachment proceedings because that would imply that O legitimately held the office in the first place, and that impeachment was an attempt to remove him.
Of course this presupposes the notion that Biden and Congress were actually interested in following the Constitution, so it's all really a moot point.