Evidence? That's a bold claim, and not true at all if you look at the length of time political parties have continuously held the White house. There's plenty of examples to the contrary, and nothing statistically significant about the number of 8 year terms followed by a different party that would indicate "impossibility": https://en.wikipedia.org/wiki/Political_power_in_the_United_...
However, a plausible explanation for why there is a bit lower chance (roughly 1/3) of re-electing your party after 8 years is that roughly 2/3rds of our two term presidents have failed to deliver on promises (or failed in other ways) to the American people, and Obama happens to fit that explanation very well.