Republicans say the White House, after badly mismanaging its messaging on sequestration, now has no choice but to accept the lower spending levels, which is a significantly positive outcome for Republicans, both from a political and policy perspective. “It’s a big deal,” says a senior GOP aide. “This was a necessary win for Republicans. It’s not sufficient, but absolutely a necessary win.”

“Americans understand that if the sequester get replaced, it gets replaced with spending cuts, not tax hikes” says another GOP aide. “They’ve resigned themselves to lower spending levels.”

The fight over the sequester was a fight the GOP wanted to have, and a key component of a multi-step political strategy hammered out weeks ago at the House Republican retreat in Williamsburg, Va. The recent showdown was precipitated by the decision to delay (until May) another confrontation over the debt ceiling (and force the Democratic Senate to pass a budget) in the hope that the politics surrounding sequestration would be more favorable to Republicans. The American people agree with the GOP on spending cuts, one GOP aide explains, but are less thrilled about the prospect of a government shutdown, or defaulting on the national debt. “So far I think sequencing of it all has come out pretty well,” the aide says.