“A vote for cloture is a vote for Obamacare,” Mr. Cruz said.

Yet after the vote on Wednesday, Senator Mike Lee, Republican of Utah, said Mr. Cruz had never intended to oppose the motion to take up the bill, an assertion contradicted by Mr. Cruz’s words and procedural motions for days before the tally. Aides to senior Republican senators fumed that they had been deluged by conservative activists pressing for a “no” vote.

On the Democratic side, Senator Charles E. Schumer of New York said that “the only reason Ted Cruz switched to ‘yes’ is that he would have had so few people voting with him it would have been embarrassing.”

Mr. Reid greeted the conclusion of Mr. Cruz’s performance by declaring it “a big waste of time.”

While heads spun on Capitol Hill over Mr. Cruz’s performance, Treasury Secretary Jacob J. Lew on Wednesday handed Congress a new deadline to worry about: Oct. 17. That is when the Treasury will have only $30 billion of cash on hand, putting the United States on the precipice of an unprecedented default, unless Congress raises the government’s statutory borrowing limit. It is the first hard deadline offered by the Treasury and compounds the problems of a Congress already struggling to keep the government open past Monday, when much of it will run out of money.

“The president remains willing to negotiate over the future direction of fiscal policy, but he will not negotiate over whether the United States will pay its bills for past commitments,” Mr. Lew wrote in a letter to the House speaker, John A. Boehner of Ohio.