It should be the objective case because it's an object of the verb "put up", not because it heads the phrase "whomever the dems put up". Who/whom has to do with its role in its own phrase, not the larger sentence/clause. Contrast "I will vote for whoever wins the dem nomination."
It should be the objective case because it's an object of the verb "put up", not because it heads the phrase "whomever the dems put up". Who/whom has to do with its role in its own phrase, not the larger sentence/clause. Contrast "I will vote for whoever wins the dem nomination."