The president and his negotiators believe they worked out a deal that allowed Republicans to claim big spending cuts even as the reality was far more modest.

They settled on a plan, which in essence would penalize Republicans’ most cherished spending programs if they failed to follow the contours of the agreement. Then they forced Republicans to include that plan in the legislative text codifying the deal.

The way administration officials see it, the full final agreement’s spending cuts are nothing worse than they would have expected in regular appropriations bills passed by a divided Congress. They agreed to structure the cuts so they appeared to save $1.5 trillion over a decade in the eyes of the nonpartisan Congressional Budget Office. But thanks to the side deals — including some accounting tricks — White House officials estimate that the actual cuts could total as little as $136 billion over the two enforceable years of the spending caps that are central to the agreement.

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