In Kentucky, home of the Senate Republican leader, Mitch McConnell, residents woke up on Monday to news articles like these: Widespread government spending cuts that begin on Friday will cost 21,484 jobs in the state. A construction project at Fort Knox will come to a halt. Three airports may endure partial shutdowns. Nearly $12 million in grants to public schools would be cut, putting at risk the jobs of 160 teachers and aides. More than 1,000 children would lose access to Head Start.

The White House released warnings for every state on Sunday in the hope that angry voters would besiege Republican lawmakers like Mr. McConnell and the House speaker, John Boehner, to stop the $85 billion in cuts, known as a sequester. President Obama wants to replace the sequester with a mix of tax increases on the rich and less damaging spending reductions. Republicans say they won’t consider any proposal that isn’t all cuts, so the sequester is all but certain to begin this week.

The White House strategy on the sequester was built around a familiar miscalculation about Republicans. It assumed that, in the end, they would be reasonable and negotiate a realistic alternative to indiscriminate cuts. Because the reductions hurt defense programs long held sacrosanct by Republicans, the White House thought it had leverage that would reduce the damage to the domestic programs favored by Democrats.

It turns out, though, that the defense hawks in the party are outnumbered. More Republicans seem to care about reducing spending at all costs, and the prospect of damaging vital government programs does not seem to bother them. “Fiscal questions trump defense in a way they never would have after 9/11,” Representative Tom Cole, a Republican of Oklahoma, told The Times. “But the war in Iraq is over. Troops are coming home from Afghanistan, and we want to secure the cuts.”