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Senate Majority Leader Harry Reid, Nevada Democrat, has promised to work with Republicans to ward off sequestration. But he has insisted that any compromise include tax increases — setting up a clash with Republicans, who are in no mood to concede on the issue again after giving in to Mr. Obama’s demand to include tax increases as part of the New Year’s Eve deal to avoid the “fiscal cliff.”

Americans “believe that there could be a better way of dealing with defense [cuts] than this meat cleaver that sequestration does,” Mr. Reid told reporters Tuesday. “But part of it, the American people agree, should be the wealthiest people in America paying a little bit more, and there should be a balance of spending cuts and revenue.”

Dave Boyer contributed to this article, which is based in part on wire service reports.