“When we focus on economic mobility, that’s a conversation that unites us,” Jack Markell, the popular two-term Delaware governor and a self-styled centrist, told me. “If it’s about inequality, it’s a conversation that has the potential of dividing us.” Markell says that middle-class voters hear in the crusade against “inequality” a desire to equalize people rather than make everyone better off.

In de Blasio’s resounding win and the burgeoning celebrity of Massachusetts Senator Elizabeth Warren, many have seen a new flowering of liberalism. Peter Beinart, writing in The Daily Beast in September, argued that the Millennial generation, accustomed to diversity and fired by a sense of economic injustice, is pushing the electorate leftward. The New York Times and The New Republic have both portrayed Warren, with her calls for expanding entitlements and cracking down on Wall Street, as a counterpoint to the cautious centrism of Hillary Clinton.

Stan Greenberg, a longtime Democratic pollster who advised de Blasio’s campaign, insists that most Democrats, including Obama, are on the same page as Warren. In both presidential elections, he noted, “Obama ran on a future for the middle class of restoring prosperity, raising taxes on the wealthy, and an investment agenda. That’s the mainstream of the Democratic Party; it’s the mainstream of the country.”

But the trumpeting of a new progressive era triggers traumatic flashbacks for the Democratic warriors of a previous generation. They remember the party’s many years of nominating liberal candidates like Walter Mondale—and losing badly. So the centrists recently fired back. In a December 2 Wall Street Journal op-ed, Cowan and another Third Way official argued that “populism” was a dead end for Democrats. They urged the party to demonstrate fiscal responsibility by embracing entitlement reform.

“There is a very large faction within the Democratic Party that wants to go back in time,” Cowan told me. “They want to take what we did in the 20th century and do more of it. They want to re-unionize the entire country, unwind the trade deals of the last couple of decades, and not just preserve but expand entitlements. Even if we could afford that, it wouldn’t solve most of the problems of the middle class.”

The backlash to the Cowan op-ed was swift and forceful. The next day, Warren wrote a letter to several banks asking them to disclose their donations to think tanks that was widely seen as a swipe at Third Way, though it didn’t mention the group explicitly. Progressives called on Democratic officeholders to repudiate the op-ed, which many did, and to cut their ties to Third Way, which most did not. The liberal group MoveOn.org released a television ad responding to Third Way’s criticism and pointedly aired it only in the Washington, D.C., market. “Third Way and many of the Beltway insiders it works to influence are simply out of touch with the American public on Social Security,” MoveOn’s Ilya Sheyman said.