Several of the Republican candidates have had embarassing electoral defeats:
Romney, obviously, has his loss to Ted Kennedy in 1994 (and his platform is more embarrassing for him than the fact that he lost by a Santorum-esque margin).
Then, after winning the 2002 gubernatorial election by a hair (and without a majority of the vote) despite outspending his opponent, Romney became so unpopular that he didn't even bother running for re-election. And when he ran for the Republican nomination instead, he suffered humiliating defeats in Iowa and New Hampshire despite (once again) outspending his opponents and despite by most accounts having the best-organized campaign.
Ron Paul's 1988 third party candidacy deserves mention, if only for the fact that it led to
this. (It's helpful to Paul that it's been over a quarter century since he ran as a Libertarian and made his attempt at the Senate.)
It took Gingrich three attempts to win a seat in the house, and he came within a few hundred votes of losing his seat in 1990. He also was forced out of his seat by his colleagues, which seems just as embarrassing as any electoral defeat.
Rick Perry has never lost an election, but he's had a surprising number of close calls, the last two gubernatorial elections in particular.
