In the end, it came down to two 70-year-old men, talking on the phone.

They are not the most powerful men in Washington: Each, in his own way, is a second fiddle. Joseph R. Biden is vice president. Mitch McConnell (R-Ky.) is the Senate minority leader, in charge only of the senators who are not in charge.

But these two men — rivals, colleagues and wary friends for almost 28 years — were the ones called upon to try to close a deal that had eluded all the negotiators before them.

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