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“If it had to be used, it would have turned the gridlock into a meltdown,” said Sen. Carl Levin, Michigan Democrat. “It would have made the gridlock that we’ve seen so far look like a Sunday school picnic.”

Democrats said Mr. Reid could have mustered the votes and the threat helped push Republicans to strike the deal.

“He was prepared to do it,” Mr. Durbin said. “Frankly, the only way you can reach this compromise in negotiation is if the other side believes you’re serious. And Harry Reid had the votes.”

He said if the new agreement doesn’t work, Mr. Reid can always use the 51-vote strategy in the future.