The vote, however, exposes the true priorities of the Republicans. No Senate Republican agreed to support the middle-class tax cut by itself because they insisted that the rich get one, too. (Actually, the rich would have gotten a tax cut on their first quarter-million of income, but, apparently, that wasn’t enough.) Forty-four Republicans (and one Democrat) voted for an alternative bill that would give wildly generous estate tax breaks to a few of the richest American heirs at a cost of $119 billion to the deficit.

And those 44 Republicans also voted to raise taxes on 13 million low- and moderate-income working families. Though it seems unbelievable on a day when Republicans tried to be so generous to their wealthiest contributors, they voted for a bill that would end the child tax credit for nine million families that make less than $13,300, costing some of the nation’s most struggling households $854 a year. Another four million families would be affected by the Republican vote to reduce both the earned income tax credit and the middle-class credit for college tuition.

For these families, the party of Grover Norquist’s no-tax-hike pledge has no sympathy. The tax credits were part of Mr. Obama’s 2009 stimulus law and thus have no currency with Republicans, several of whom said on the Senate floor on Wednesday that they were only intended to be temporary.

But the Bush tax cuts were also temporary. They first expired in 2010, but Mr. Obama and the Democrats agreed to Republican demands to extend them for two years or risk hurting the middle class with a tax increase. This time, Democrats say they are willing to stand up to hostage-taking and let all the tax cuts expire on New Year’s Day, then reinstate those for the middle class.

That step will probably be necessary once the bill passed by the Senate on Wednesday goes to the Republican-controlled House, which will kill it. The official justification will surely be that all revenue bills have to originate in the House, but that’s a procedural barrier that could easily have been sidestepped if Senator Mitch McConnell, the Republican leader, hadn’t refused to do so.