On the eve of a demonstration over the death of a black Staten Island man in police custody, organizers were making sure the official signs carried messages that, while protesting aggressive policing, did not castigate the New York Police Department.

Signs reading “Support NYPD. Stop Police Brutality” would be dotted among those reading “Respect Human Rights” and “Justice for Eric Garner” at the march on Saturday, said Chelsea-Lyn Rudder, a spokeswoman for 1199 S.E.I.U. United Healthcare Workers East, one of several labor unions participating in the protest.

The careful sign-making came as the labor unions faced backlash from police unions, over both their involvement in general and because the demonstration, on Staten Island, was led by the Rev. Al Sharpton, a lightning rod in police-community relations in New York City.

Specifically, the United Federation of Teachers was facing off with some of its own members who demanded the resignation of its president, Michael Mulgrew, over the union’s involvement and threatened to end contributions to the group’s political action committee. When the union announced last week that it would be joining the march its Facebook page filled with more than 1,000 comments, along with thousands of replies, that were overwhelmingly negative.