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Mr. Tanner said there was a chance to fight for something more specific such as a one-year delay in the individual mandate requiring all Americans to obtain coverage, but there was never much likelihood Mr. Obama or Democrats were going to accept an end of the Affordable Care Act.

“The Republicans essentially gave up their opening bid early on and then sort of scrambled to try to throw this together at the end,” he said, adding that the outcome is “going to be very messy” for all sides.

But those fighting alongside Mr. Cruz said GOP leaders should listen to the voters who have rallied around the call to defund the health care law.

“What I think you’re seeing from folks is the frustration that Washington isn’t driving the agenda anymore. The folks outside Washington are driving the agenda,” said Dan Holler, communications director at Heritage Action for America. “Back in July, nobody expected Obamacare to be the big thing this fall. And now it’s the only thing. And that’s because lawmakers’ constituents rose up and demanded it.”

Mr. Holler said the shape of the debate is already a kind of victory because it’s focused on health care, not on dollars.

“The fight on the year-end spending bill has been on Obamacare. Harry Reid, Barack Obama, the appropriators, all wanted this fight to be on government spending levels — how high can we go, can we turn off the sequesters,” Mr. Holler said. “Because conservatives are playing offense on Obamacare, they weren’t put in a position where they had to play defense on spending.”

Still, Mr. McKenna said there is collateral damage from Mr. Cruz’s approach.

“What’s happened is he’s sucked all the oxygen out of the room for the last six months when we could have been talking about legitimate ways to fix it, or legitimate ways to postpone the individual mandate,” he said.

Mr. McKenna said major changes will have to wait until more of the law goes into effect and people begin to rebel against its consequences. The wait, he said, makes it “take a lot longer and be more difficult.”

The defunding fight has been painful for Republican leaders. In the House, they had to scrap their preferred strategy and pass a real defunding bill, demanded by their rank and file.

In the Senate, however, the parliamentary mess has given GOP leaders the ability to vote for defunding Obamacare while knowing they are likely to lose the fight.

Mr. Cruz is expected to be one of several senators exploring a bid for the GOP presidential nomination in 2016, along with Sens. Rand Paul of Kentucky and Marco Rubio of Florida.

Mr. Rubio made his own mark earlier this year, successfully helping push an immigration bill through the Senate, though wounding his own standing with Republican primary voters.

By contrast, Mr. Cruz, who appears poised to fail in his legislative effort, likely will be rewarded by GOP voters.

Mr. McKenna said the two senators share a link in their willingness to strike out on their own and defy party leaders.

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