Unions have no necessary connection to the process.
The elected official's opponent in the following election simply runs a "JOHN SMITH IS SOFT ON CRIME, JOHN SMITH IS BAD FOR US AND OUR FAMILIES" campaign, and people who think public-sector unions are the devil will still vote for the opponent, because now you're pressing their bias (which is in favor of "tough on crime, lock 'em all up and throw away the key").
The elected official's opponent in the following election simply runs a "JOHN SMITH IS SOFT ON CRIME, JOHN SMITH IS BAD FOR US AND OUR FAMILIES" campaign, and people who think public-sector unions are the devil will still vote for the opponent, because now you're pressing their bias (which is in favor of "tough on crime, lock 'em all up and throw away the key").