A group of protesters, some with costumes and snarky stage names, gathered Wednesday on the swank Main Street of Southampton, N.Y., not far from the summer home of one of the private equity industry's leaders, Henry Kravis of Kohlberg Kravis Roberts.  Slinging slogans like "protect the emerging plutocracy" and cheerfully greeting passersby with "have a wonderful wealthy day," these activists — tongues firmly planted in cheeks — demanded more tax relief for private equity fund managers.

Their real objective, of course, was exactly the opposite.

Wednesday's protest was organized by the Service Employees International Union, which represents nearly two million workers, and the Working Families Project of New York.

It was hardly a mass uprising: The eight or so participants were outnumbered by media covering the event. But the performance marked a new level of showmanship (and sarcasm) in the escalating debate over a bill to raise taxes on "carried interest," a major source of buyout fund managers' profits.

His effort to blaze a new trail appears to be modeled less on labor leaders of the past than on a civil-rights leader: Jesse Jackson. Their common tactic: Attack first, then engage — with a hand out for the ultimate payoff.

For some on the receiving end, this feels like a shakedown, though none of the private-equity leaders I spoke with will say so on the record. But Mr. Stern is unapologetic. Indeed, he blames business for encouraging labor to behave badly. "They've trained us wrongly," he says. "We tend to get ignored or caricatured, and sent to the human-resources department when we call. The CEO says, 'Will someone take care of these guys?' Not until we do something they find 'unfair' will they talk to us."

"It's like your children," he adds. "If they behave and get no reaction, then they'll cry."