Members of the group worried that, with the end of the Bill Clinton era, the Democratic Party’s centrist wing had lost its way. Over sodas, they pitched a new think tank named for Clinton’s political philosophy, Third Way.

Fast forward a decade: The philosophy, sketched out privately at the Boston office of Brown Rudnick,
is now at the center of an intense struggle for the soul of the Democratic Party.

Third Way, backed by Wall Street titans, corporate money, and congressional allies, is publicly warning against divisive “soak-the-rich” politics voiced by populist Democrats. Its target: Elizabeth Warren, the Massachusetts senator whose rise to power two years ago helped galvanize Democratic grass roots against Wall Street and pushed the issue of income inequality to the forefront.

Two-thirds of its 31 trustees have held senior leadership positions in investment funds or big banks or served in some other capacity on Wall Street.

Third Way leaders are extremely sensitive to questions and criticism about their sources of funding. The real issue, Third Way says, is that harsh populist positions and rhetoric are damaging the Democratic Party.

“It goes back to what Bill Clinton said, which is ‘You can’t love the job and hate the job creators,’?” said Matt Bennett, Third Way’s vice president for public affairs and one of its cofounders. “Vilification of industry isn’t helping Democrats.”

Their overarching emphasis is on solidifying political support among the middle class. Where they differ from many Democrats is how they plan to appeal to the vast middle: reduce deficits and cut spending growth on such entitlements as Social Security and Medicare.

They insist on deficit reduction and entitlement cuts as conditions for key tax hikes on the wealthy.

“Raising taxes is absolutely essential, but it is not sufficient from our perspective,” Cowan said in an interview, in which he also said the group advocated strongly for Obama’s health care law and the deal that ended the fiscal cliff, both of which included tax hikes on the wealthy.

“If the Democratic Party stands only for raising taxes on the wealthy, not for actually making entitlement reforms and other spending cuts,’’ he said, “then the other half of the equation will never happen.”

The battle over money and influence has now moved to the 2016 presidential election, and the competition between parties for the financial favors of Wall Street executives will be fierce.

Though Third Way’s salvo against Warren in The Wall Street Journal became a seminal moment in its fight against Democratic populism, the group is now very sensitive about the topic and will not even discuss why they chose to wage it.

Robert Reich, Clinton’s former labor secretary, who has become a leading Wall Street critic, argued that there are several issues Democrats are unwilling to tackle because of Wall Street’s grip on the party — including tax breaks for hedge fund managers, transaction taxes for high-speed traders, limits on the size of banks, and income tax rates for high earners.

“At some point it becomes a Faustian bargain,” he said. “The financial dependence on Wall Street effectively ties the hands of the Democratic Party.”

But moderate Democrats worry the party is doomed to lose general elections if candidates are perceived as antibusiness in an effort to win over activists on the hard left.

“That really has never generated a hell of a lot of support on Election Day,” Daley said.