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Mr. Cruz and his allies, though, argue that is tantamount to voting for Obamacare funding. Indeed, Republicans have regularly led filibusters before when they’ve argued Democrats structured an unfair floor debate.

Despite their defeat, Mr. Cruz and his chief filibuster ally, Sen. Mike Lee, said the fight goes on.

“This vote is not the end. It’s not even the beginning of the end. It’s the end of the beginning,” Mr. Lee said. “The American people will always have the final word.”