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Ford O’Connell, a GOP strategist, said that the Cruz approach could come back to haunt it in the next spending battle and the 2014 election.

“All or nothing was really a dumb move,” Mr. O’Connell said. “Because they decided to shoot for the moon, they came out the loser, the GOP brand is at an all-time low and somehow Obamacare has increased in public favorability.”

Mr. Cruz, though, struck a defiant note Wednesday, criticizing members of both parties for reaching a bipartisan deal to fund government operations and Obamacare.

“Unfortunately, once again, it appears the Washington establishment is refusing to listen to the American people,” he said, adding, “The House of Representatives has taken a bold stance listening to the American people. But unfortunately, the United States Senate has refused to do likewise.”

Sen. Kelly Ayotte, New Hampshire Republican, said she never supported Mr. Cruz’s strategy and took umbrage with his assertion that she and other Senators who backed the bipartisan deal were out of step with the public.

“I have been listening to people in New Hampshire, and I’ve had a lot of people that feel as passionate as I do about repealing Obamacare that have said to me that they don’t see how this is going to succeed,” Mrs. Ayotte said of the Cruz-led approach. “So, I think we can both oppose Obamacare, but we can have a legitimate disagreement over a strategy on how to move forward”

“If we learned nothing else from this whole exercise, I hope we learn that we shouldn’t get behind a strategy that cannot succeed,” she added.

Sen. John McCain, Arizona Republican, said he has a different sense than Mr. Cruz of what the American public wants from Congress.”Every reputable poll that I know of says that the American people are blaming us for the shutdown of the government, and they don’t want the government shutdown — but everybody is entitled to their opinion,” Mr. McCain said.

“I hope we learned a lesson,” he said. “As you know I predicted it three weeks ago, I said I know how the movie ends — and I wish I was wrong.