"Nominee" is the antecedent of "whomever" in your sentence, so you described it incorrectly when you said that the word whomever "is still the anteceedent[sic] of nominee."

One clue on that score should have been the fact that the ANTEcedent comes before the pronoun that refers to that antecedent.  Ante means before.  Get it?

More importantly, the case of the pronoun (either nominative or objective) is NOT dependent on the case of its antecedent.  The pronoun's case depends upon the use of the pronoun in its own clause.

Therefore, the correct way to express the above is indeed:  "Get behind the Dem nominee, whoever he is."  Whoever is a predicate nominative in the dependent clause.

So you are the one who is confused.  Your assertion that "any pronoun for nominee has to be in objective form because nominee is the object" is just plain wrong.

How does this sound to you?

  I will vote for the candidate whom speaks best in the debate.

Sounds wrong, doesn't it?  Although the antecedent is candidate, and candidate is objective here, there's no way that "whom" can serve as the subject for the dependent clause.

The correct version would read:  I will vote for the candidate who speaks best in the debate.

Alternately, you might say:  I will vote for the candidate whom the party chooses.

There, whom is correct, because it is the object of the clause -- "The party chooses whom?"

So please, heed your own warnings, and don't make yourself look any stupider.