Family names can be accompanied either by the definite article the ("the Smiths") or by the zero article ("Smiths"). However, these two constructions mean slightly different things.
Americans are tired of the Bushes.
This construction suggests that Americans are tired of "the Bushes" as a collective entity - that is, Americans are tired of the whole goshdarned Bush family, taken as a single group.
Americans are tired of Bushes.
This construction, as Edwin Ashworth eloquently points out, is "hedged" and "distancing" - it suggests that Americans are tired of various "Bushes", each taken individually, without requiring the speaker (a Bush) to assert that Americans are tired of a group that includes her.
That is, Americans might be tired of George H. W. Bush, and also tired of George W. Bush, and also tired of Jeb Bush, and maybe even tired of Prescott Bush - but Americans are not necessarily tired of Bushes as a whole; just some Bushes in particular.