Sen. Cruz: This is our best opportunity to defeat Obamacare

Senator Ted Cruz
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Senator Ted Cruz, R-Tx., says there is only one way to defeat the Affordable Care Act, and it's not another attempt to repeal the law.

"The reason why I'm focused on defunding Obamacare is that it's the only strategy that anyone has suggested that has any chance of success," he said on CNBC's "The Kudlow Report." "This is our best opportunity to defeat Obamacare, and it may be our last opportunity."

Over the five-week Senate recess, Sen. Cruz will embark on a series of town hall meetings across the country to help build support to defund The Affordable Care Act.

"The purpose of the tour is to mobilize and energy the American people. If ordinary Washington rules apply, we can't win this fight."

Cruz said there is a bipartisan agreement that Obamacare is not working, but Congress does not have the 41 Senate and 218 House Republican votes necessary to repeal the law.

"The most important Constitutional check that Congress has on an overreaching President is the Power of the purse. If Republicans stand together, we can actually succeed in defunding it."

Cruz said the legislation to defund the Affordable Care Act, would not have no effect on the debt ceiling as it only eliminates all federal funding, mandatory or discretionary, for the law itself.

"The House of Representatives should pass a continuing resolution that funds the entirety of the federal government except for Obamacare," hes aid. "If that passed Obama would be entirely defunded and halted in its tracks."

Rep. Marsha Blackburn, R-TN, said she sponsors the movement to defund Obamacare in the House, but she is also pushing more sweeping approach: "delay, defund, repeal, replace."

"If you want to make certain that you are to be able to finally get rid of this bill, to repeal it and replace it with things that are patient-centered and market driven, then let's delay all programs, let's delay all taxes, let's defund all of these programs and benefits and then get this off the books," Blackburn said.

But some Obamacare supporters say Republicans' strategy puts the rest of the federal budget and debt ceiling at risk in yet another attempt to get rid of the Affordable Care Act.

"There's a lot of folks that are using any tact they can to unravel the Obamacare bill," Rep. Peter Welch, D-MA, said. "They're against it and they're very explicit about that. But we've got to get on with the program. The burden on those of us who supported it is to listen to folks, the providers, the hospitals, the businesses, to understand what the implementation challenges are."

—By CNBC Associate Producer Elizabeth Schulze. Follow her on Twitter @ESchulze9