The formal name of one Chicago-based labor group is a mouth full: Liquor & Wine Sales Representatives – Tire, Plastic, and Allied Workers Union Local 3.

But in shorthand, it’s known simply as “the Duffs.”

The family – which includes members who were once prominent in organized crime, business and political circles – is quietly staking a flag, or two, in the governor’s race, with Local 3’s political-action committee donating $1,000 to Gov. Pat Quinn’s campaign in recent weeks, and another $1,000 to failed GOP hopeful Kirk Dillard before last month’s primary, state campaign records show.

The president of Local 3, Patrick Duff, has kept his nose clean over the years so far as we can tell. But his brother, Jack Duff III, has a troubling background that includes reputed mob ties and alleged involvement in a bookmaking operation, according to public records. Jack Duff III was secretary-treasurer of Local 3 for many years. U.S. Department of Labor records, however, indicate he may have left the post in 2013.

Neither Patrick Duff nor Jack Duff III could be reached for comment.

Their late father, Jack Duff Jr., once ran the union and maintained interesting connections – testifying at a 1960 tax-fraud trial on behalf of mob boss Tony Accardo, whom he described as a friend, and socializing with now-former Mayor Richard M. Daley, for whom the Duffs raised campaign money.

Their brother James Duff once worked for the union but is better known for going to prison in the mid-2000s for a Daley-era minority-contracting scheme. Duff-owned janitorial and staffing businesses secured more than $100 million in city government-related contracts by pretending to be run by a woman and minorities – which gave them a leg up in the procurement process.

So, with all that as a backdrop, we were curious about Local 3’s donation to Dillard, recorded by the Illinois State Board of Elections on Dec. 31, 2013.

A Dillard spokesman said, “Kirk doesn’t know the Duffs” and has “no clue about where the money came from,” adding it “wasn’t solicited.”

The campaign also noted via email that the Local 3 PAC “gave to other candidates – both Dem and GOP – besides us.”

Now he’s giving back?

Which is certainly true. Quinn – the Democrat Dillard would have faced in the November general election if he’d beaten Republican Bruce Rauner in the primary – not only took $1,000 recently from Local 3, he’s accepted $3,600 in campaign cash from Local 3 dating back to 2002, state records show.

A Quinn campaign spokeswoman told us Quinn’s camp is now returning the $3,600 out of “an abundance of caution.”

Ok, but why?

We couldn’t get an answer from the spokeswoman. And Tom Quinn, the governor’s lawyer-brother and campaign chairman, didn’t return repeated calls.

‘On with my life’

All of this might make you wonder about James Duff, the brother sentenced to prison in 2005 after being found guilty in that minority-contracting scam.

He’s out of prison now and almost 56.

He did federal time in Yankton, S.D.; La Tuna, Tex.; and Duluth, Minn. Then he hit a halfway house in early 2013 before doing five months of home confinement that ended in July, according to the U.S. Bureau of Prisons. He’s now on three years of supervision, basically probation.

We caught up with him after tracking down a cell phone number. We asked where he’s working.

He’s known as a tough guy, a hulking former college football player, but he was exceedingly polite on the phone, declining to discuss his job situation except to say, “I’m not working for Local 3 . . . I’ve got nothing to do with that.”

Before hanging up, James Duff said, “I’m just trying to get on with my life.”

This column — a new regular feature called The Public Eye, appearing on the Chicago Sun-Times’ political portal Early & Often — was written and reported by the Better Government Association’s Robert Herguth and Patrick Rehkamp. They can be reached at rherguth@bettergov.org or (312) 821-9030.