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“Surely, you can find a little more than 2 percent to cut from the federal budget,” Mr. McConnell said. “And surely you can do it without raining down a phony Armageddon on American families. They had to find ways to cope with 2 percent less in their paychecks last month after the payroll tax went back up. Why can’t Washington?”

He concluded, “The time for games is over.”

But with negotiators’ first meeting to take place on the same day as the cuts are starting, nobody really believes the games have ended.