It is no secret that the Obama administration’s Syria policy, to the extent that one exists, is failing.

Now the man with the unenviable task of implementing that policy, Secretary of State John F. Kerry, has acknowledged as much, according to two U.S. senators who spoke with him Sunday, John McCain (R-Ariz.) and Lindsey O. Graham (R-S.C.).

Kerry said that the Geneva negotiating process hasn’t delivered, they said, and that new approaches are needed.

“He acknowledged that the chemical weapons [removal] is being slow-rolled, the Russians continue to supply arms, [and] we are at a point now where we are going to have to change our strategy,” Graham said.

The secretary spoke favorably about arming and training the rebels, Graham added.

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Both senators are longtime critics of the administration’s Syria policy. Presented with a summary of Kerry’s reported statements to them and about a dozen other members of Congress, Kerry’s spokeswoman, Jennifer Psaki, called it a “mischaracterization.”

“No one in this administration thinks we’re doing enough until the humanitarian crisis has been solved and the civil war ended,” she said. “That is no different from the message Secretary Kerry conveyed during the private meeting.”

Psaki, who attended the meeting, said Kerry did not raise the prospect of lethal assistance for the rebels. “This is a case of members projecting what they want to hear and not stating the accurate facts of what was discussed,” she said.

In fact, more than a year ago Kerry openly advocated changing the dynamics in Syria so that dictator Bashar al-Assad would have an incentive to negotiate. But the White House vetoed any serious training or arming of the rebels. That left Kerry beseeching Russia to persuade Assad to make concessions even as the dictator was gaining on the battlefield. Not surprisingly, that hasn’t worked.

“We haven’t achieved anything,” U.N. envoy Lakhdar Brahimi reported over the weekend to the Munich security conference, which Kerry and the members of Congress also attended. “In Homs [where civilians have been cut off from any aid] we haven’t been able to do anything. And about prisoners, disappeared people, kidnapped people, again we haven’t achieved anything.”

The result: Syria has become “the worst humanitarian crisis at least since the Rwanda genocide,” António Guterres, chief of the U.N. refu­gee agency, told the conference.

More than 100,000 people have been killed. Nine million Syrians — more than a third of the country — have been forced from their homes. Assad is blocking aid and deliberately starving hundreds of thousands of his countrymen.

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It is “a strategy of war crimes,” said Kenneth Roth, head of Human Rights Watch, “to make life as miserable as possible for civilians in opposition- ­controlled areas.” He showed video footage of Assad forces bombing bakeries and people waiting in line for bread.

Recently a trove of photographs showed 11,000 corpses — prisoners starved and tortured to death by the regime.

President Obama pronounced 2½ years ago that “the time has come for President Assad to step aside.” Since then, as the humanitarian disaster has escalated, the U.S. president has been inert.

Now, though, a new factor has emerged. Last week, in Senate testimony that got less attention than it deserved, Obama’s director of national intelligence, James Clapper, said Syria “is becoming a center of radical extremism and a potential threat to the homeland.”

Havens in Syria, in other words, could play the same role that Afghan refuges offered al-Qaeda before 9/11. As the West cold-shouldered moderate and secular forces, extremist ranks have swelled in Syria to as many as 26,000, including 7,000 foreigners, Clapper said.

It was that testimony that prompted McCain and Graham to talk to me and two other journalists, Jeffrey Goldberg of Bloomberg View and Josh Rogin of the Daily Beast, about Kerry’s remarks, as we flew back from Munich. The senators hope that the assessment of a growing direct threat, along with stark evidence of organized torture, could impel a shift in direction.

“Our director of national intelligence said that these people in Syria are planning attacks against the United States,” McCain said. “Kerry confirmed that. . . . Maybe those two disturbing facts about the results of the war in Syria could maybe help them think they ought to change their policy.”

The two senators don’t agree on what that change should be. Neither favors sending U.S. troops. Graham wants to see U.S. drones attacking al-Qaeda havens. McCain would rather help establish a safe zone in which to train the Free Syrian Army and care for refugees, protected by Patriot missiles based in Turkey.

A third route would be for the administration to put U.S. muscle behind a U.N. demand that Assad at least permit food and blankets to reach starving, freezing families.

Can Kerry bring his boss around to a more activist policy? Obama has doubted that the United States could intervene in such a messy conflict without making things worse. He reportedly worries that even a limited commitment would inexorably suck the nation into something deeper. There certainly is no public clamor to intervene.

On the other hand, even as he has pulled back from Iraq and Afghanistan, Obama has proclaimed the war against al-Qaeda a national security imperative.

“So to me,” Graham said, “it’s a choice of, do we hit them after they hit us, or do we hit them before they hit us?”

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