Passionate supporters of Senator Bernie Sanders awoke enraged on Tuesday after learning that his slim hopes for winning the Democratic presidential nomination had been effectively dashed as a batch of superdelegates revealed their support for Hillary Clinton.

After months of dancing around the phrase, news organizations on Monday night finally bestowed a much-coveted label on Mrs. Clinton: presumptive nominee.

The Sanders campaign immediately assailed the media for rushing the process and undermining the will of voters who were set to head to the polls in six states on Tuesday.

In a late-night fund-raising email, Jeff Weaver, Mr. Sanders’s campaign manager, urged voters to defy the pundits and deliver a stunning series of victories for the Vermont senator.