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If you wonder how historians can argue endlessly about what happened long ago — did Lincoln fight to free the slaves or to preserve the union, say — look at how we can disagree about what happened just during the past four years, while we all were watching.

On the left it is now accepted that President Obama came into office trying to bridge the blue-red divide, was played for a sucker time and again, and finally, belatedly, came to realize that there’s no compromising with this bunch of far-right Republicans.

The right, meanwhile, is equally convinced that Obama came into office with a far-left agenda and pushed it as hard as he could, retreating tactically only when he was forced to do so and showing his true colors once again in his second inaugural address.

You can write a coherent history either way.

Here’s how the left (and many in the White House) would see it:

Obama pursued two major initiatives in his first term and on both bent over backward to accommodate Republican sensibilities. His first, the stimulus bill, was one-third tax cuts, which conservatives preferred to spending. His second, on health care, eschewed not only the single-payer model that has worked in other countries but even a “public option,” choosing instead to work entirely through private insurance firms. He adopted the individual mandate that had been developed by the Heritage Foundation. He delayed passage month after month while Republican senators dangled the possibility of cooperation that never came.

To achieve a fiscal compromise, Obama agreed in 2011 negotiations with House Speaker John Boehner to changes in Social Security that would be anathema to liberals, but Boehner walked away from the talks. In December 2012 the speaker walked away again, proving with his ill-fated Plan B that he could not deliver his caucus. The Republican leader in the Senate, meanwhile, listed Obama’s defeat as his top priority and, as if to punctuate the point, supported a fiscal debt commission until Obama also supported it, at which point the leader, Mitch McConnell of Kentucky, became an opponent.

Here’s how the right might describe the same four years:

Obama’s first project was a Democratic-designed stimulus bill that was, in the words of one admiring chronicler, Michael Grunwald, “astonishingly big . . . more than 50 percent bigger than the entire New Deal . . . America’s biggest foray into industrial policy since FDR.” His health-care bill represented the largest new entitlement since the Great Society. It was designed, again, by Democrats alone. And when voters showed their disdain for it, by electing a Republican senator in a special election in liberal Massachusetts, thereby depriving Obama of his 60-vote supermajority, he rammed the bill through the Senate using “reconciliation,” a maneuver that had been designed for budget-related legislation.

To achieve a fiscal compromise, Boehner agreed to $800 billion in new tax revenue, which was anathema to conservatives — at which point Obama moved the goal posts and asked for $1.2 trillion. The president installed two of the most liberal justices of the modern era on the Supreme Court and urged them to use “empathy” in judging. He promoted a climate-change bill that would have remade the U.S. economy, backing off only when it became clear Congress would not go along.

Both histories are factually correct. That coherent accounts can be written either way ought to suggest to partisans that neither version is quite the slam-dunk they imagine.

At a minimum, it ought to propel the White House to continue acting in the national interest, whichever party that seems to serve. And for a long time, Obama has said the national interest requires both revenue increases and reform of entitlement programs.

“The real problem with our long-term deficit actually has to do with our entitlement obligations and the fact that historically if our revenues range between 18 and 20 percent of GDP, they are now at 16,” the president told the Post editorial board in January 2009. “We’re going to have to shape a bargain. This, by the way, is where there are going to be some very difficult choices, and issues of sacrifice and responsibility and duty are going to come in, because what we have done is kicked this can down the road. We’re now at the end of the road. And we are not in a position to kick it any further.”

In a phone interview with me later that year, the president added: “It may start with Social Security because that’s, frankly, the easier one.”

The chroniclers on the right might say, looking at the past four years, Obama never meant those words. I don’t buy that. But we’ll see. He has four more years of history to write.

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