"There are some of our local union presidents who are afraid - that's the word, afraid - to give out literature for Barack Obama," Mr. McEntee, president of the American Federation of State, County and Municipal Employees, told a gathering of Illinois delegates at the Democratic National Convention last month.
"You can't vote for Barack Obama because he's black? That's the color of his skin, and that is [irrelevant]."
Mr. McEntee's concern is shared by other union leaders, who in recent weeks have made unflinching public calls to shame white members to cast aside prejudice and vote for the Illinois senator, who has the overwhelming endorsement of organized labor.
International Brotherhood of Teamsters President James P. Hoffa said unions leaders must confront racism head-on to ensure their members support Mr. Obama.
"There are people who are not going to vote for him because he's black, and we've got to hope that we can educate people to put aside their racism and to put their own interests No. 1," Mr. Hoffa said at the Democratic convention in Denver.
While organized labor nationwide has become more racially mixed in recent years, 12.5 million union members were white, 2.2 million black and 1.8 million Hispanic in 2007, according to the Bureau of Labor Statistics.
Organized labor historically has been a loyal and crucial voting bloc for the Democratic Party. In the 2004 presidential elections, Democratic Sen. John Kerry received 65 percent of the union vote, compared with 33 percent for President Bush, according to a survey by the AFL-CIO labor federation.
Unions have a heavy investment in the November elections, expecting to spend about $400 million promoting issues and candidates - almost all Democrats - this election cycle. The AFL-CIO federation alone has said it will spend more than $200 million.
Republican presidential nominee Sen. John McCain has strong appeal among many white blue-collar workers. So Obama strategists last week scrapped their initial 50-state plan to focus on key battleground states, such as Ohio, Michigan and Pennsylvania - all union strongholds.
"The Republican Party has used things such as guns and gays and God in relationship in trying to get to some blue-collar members of unions," Mr. McEntee said. "They're going to use patriotism. They're going to use some things in some kind of racial connotation in regard to Obama."
Polls show Mr. Obama leading Mr. McCain. But potential voters often mask racial prejudice in pre-election surveys, which pollsters call the "Bradley effect," after former Los Angeles Mayor Tom Bradley, a black Democrat who led by double digits in polls during his 1982 gubernatorial bid but lost on Election Day.
Adding to Mr. Obama's difficulty in wooing some union members was organized labor's initial support of New York Sen. Hillary Rodham Clinton during in the Democratic primaries.
But Mr. McEntee, whose union first supported Mrs. Clinton but now endorses Mr. Obama, said the shift to the Illinois senator has been "relatively seamless."
"There's not a hangover in regards to the candidacy of Obama," he said.
AFL-CIO Secretary-Treasurer Richard Trumka, while speaking to the United Steelworkers convention in Las Vegas in July, said Mr. Obama is the only candidate left in the presidential race who is on the side of working people.
"There's not a single good reason for any worker - especially any union member - to vote against Barack Obama," he said. "There's only one really bad reason to vote against him: because he's not white."
Chris Chafe, executive director of the Change to Win labor federation, which includes the Teamsters and the Service Employees International Union, said he doesn't think Mr. Obama's race will be a factor when his members go to the polls in November.
"My experience has always been, and polling proves it out, that union members vote overwhelming in support of the candidate who is going to do the most to help them hold on to the middle class," he said. "It's no different in this election than in any other."
• This article is based in part on wire service reports.