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Ted Cruz: 'I Didn't Say Republicans Will Win' Shutdown Fight (VIDEO)

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But the junior senator from Texas denied the premise of Crowley's question.

"Let me be clear, I didn't say Republicans will win this," he said. "Listen, I think career politicians in both parties have been part of the problem. What I said is the American people are going to win."

After being pressed by Crowley, Cruz attempted to define what a victory for the American people would look like.

"Look, what the American people want is they want our government funded and they want to stop the harms from Obamacare," Cruz said. "Obamacare is hurting millions of people. It's killing their jobs. It's forcing them into part-time work. It's driving up health insurance premiums, and it's causing millions of Americans to lose or risk losing their health insurance. That's a win for the American people is actually responding to the real harms that are coming from Obamacare."

Polls have shown that Americans overwhelmingly oppose shutting down the government to stop the Affordable Care Act. A Quinnipiac University poll released last week also found that 58 percent are opposed to Congress cutting off funding for the law. 

Reports emerged last week about a closed-door meeting where Cruz was berated by his Republican colleagues for leading the defunding push. One unnamed senator who was present described what transpired as a "lynch mob."