When I first heard the claim, I thought it was a mistake or hoax. A talking head was describing a raging war in the Democratic Party between progressives and centrists.

Centrist Democrats? Aren’t they already extinct?

Yes, they’re gone, the dodo birds of politics. But the chattering classes, needing something to chatter about and slow to face facts about their darling liberals, are just discovering that the party of Barack Obama and Bill de Blasio bears little resemblance to the party of FDR, JFK and even Bill Clinton.

Oh, please. Some of us have been saying this for years. The Democratic Party has gone so far left that late Senate stalwarts like Henry “Scoop” Jackson and Pat Moynihan, lions of liberalism but also of common sense and a strong military, must be spinning in their graves.

Or take Joe Lieberman, who got spun right out of the party. He was the Dems’ vice-presidential nominee in 2000, then drummed out as an infidel in 2006 because he didn’t bail on Iraq when the going got tough.

In New York City, conventional liberals Christine Quinn and Bill Thompson scrambled to match de Blasio’s radical “tale of two cities” narrative, but were swept aside like yesterday’s trash.

Gotham Dems who call themselves fiscal conservatives suddenly are harder to find than the proverbial hen’s tooth. They’re all progressives now, at least as measured by de Blasio’s fat coffers, stuffed by a real-estate industry that secretly says it fears him even as it offers tribute.

Another indicator is that the Rev. Al Sharpton is the Dems’ new Martin Luther King Jr. Talk about a ­decline in standards.

Remaining intra-party fights only concern how extreme the shift will be, as new militants push the Dems closer to pure socialism. Conviction politicians like Obama and de Blasio have no real interest in compromise. Look at the battle between Mass. Sen. Elizabeth Warren and Hillary Clinton.

To most sane people, Clinton no longer qualifies as a centrist. Five years ago, her muscular talk on foreign policy made her allies with Robert Gates and John McCain. But her role as front lady for the Obama appease-niks turned her muscles into fat and her policy into mush.

Yet Clinton is insufficiently committed to the movement, according to the Warren cult. And so true believers are pushing St. Elizabeth, she of the Cherokee cheekbones, to run against St. Hillary for the party mantle in 2016.

Then there’s Sen. Chuck Schumer, who could say seven years ago that he was a defense hawk. That was before he supported Obama’s abdication of global leadership and backed dovish Chuck Hagel for ­defense secretary.

Now he’s an ex-hawk, pushing to restrain Israel and rolling over for Obama’s plan to contain Iranian nukes instead of preventing them.

The lurch left is clear at home, too. The wild, incoherent rage over income inequality isn’t about creating jobs and raising the bottom. It’s about whacking top earners and punishing success. Every tax hike proves insufficient to feed the entitlement beast, so another is demanded. Too much is never enough.

Take the redistribution scheme known as ObamaCare. Virtually every Dem voted to impose a bureaucracy armed with IRS power and incomprehen­sible regulations on a health industry that, despite flaws, was the envy of the world.

The result is mass confusion, anger and the prospect of a revived Republican Party. ObamaCare also was the spark for the GOP rout in the 2010 midterms, meaning the nation still ­refuses to swallow the law nearly four years after it passed on a party-line vote.

Make no mistake, polarization is real and results from power blocs in both parties moving away from the center. But that doesn’t make them equally guilty.

Conservatives revolted over the destructive expansion of government and growing curbs on individual liberty. They take seriously, and sometimes too literally, the Constitution’s limits on federal power.

Progressives recognize almost no limits. They want a bigger government with more power, coming at the expense of individual liberty. Many want the Constitution scrapped or stretched beyond recognition.

If you’re not sure where you stand, think of Barack Obama as the litmus test. If you’re with him, you’re no hawk or centrist. You’re a progressive. But don’t confuse that with progress.

Fighting the good-gov’t fight

Gov. Cuomo is taking hits for sloppy work and too much talking by his Moreland Commission, but the panel’s vital mission remains intact. Its digging is producing fresh evidence of corruption that will increase public pressure on lawmakers to disclose conflicts of interest. Already junior legislators are breaking with leaders of both parties to agree that taxpayers deserve to know the sources of outside income.

Most important, Cuomo pledges himself to the fight.

“What is legal is the problem,” he told me. “The leaders designed a system that benefits them. That’s where they make their big money and they won’t give it up without pressure.”

He added: “We need to know who their clients are, especially the ones that have business before the state.”

One item losing steam is his call for public financing of campaigns. Court decisions are changing the legal landscape and the mayoral race saw a surge of union and independent expenditures. That genie can’t be put back in the bottle.

The debate is also irrelevant to Albany’s culture of corruption. The notion that campaign financing is the answer is like saying the crooks have to be bribed so they won’t steal.

Here’s a better idea: Let’s expose the crooks and elect honest people. That’s the purpose of the Moreland panel, and stopping halfway would embolden the thieves and waste another generation.

Cuomo gets that. “I’m on it,” he vows.

The Maker & the taker

A friend relates a parable for our times. Jesus descends to Earth and sees three men talking. He approaches the first, a blind man, touches his head, and the man can see. Jesus touches the second man, and his deafness is cured.

Jesus approaches the third man, who pushes Him away. “Leave me alone,” the man snarls. “I’m on disability and I want to keep it.”

Absolutely fib-ulous

The White House’s belated admission that President Obama did meet his “Uncle Omar,” an illegal immigrant, and lived with him, provokes a modest proposal. Since lies are routine with this administration, I suggest a day of amnesty. Pick a day — say Dec. 31 — for the administration to confess all and the slate is wiped clean.

That assumes, of course, officials can be trusted to tell the truth for a full day. That’s probably asking too much.

A story of a different color

In its story about Russian diplomats stealing Medicaid funds, The New York Times engaged in white ethnic profiling. It wrote: “Brighton Beach, Brooklyn, the center of New York City’s Russian-speaking immigrant population, has one of the highest rates of health- care fraud in the nation.”

What will the Times admit next — that blacks and Latinos commit 95 percent of city murders? Don’t hold your breath.