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He said, she said on government shutdown, Obamacare

The national debate that shut the government down played out again Tuesday morning in a heated faceoff between Rep. Debbie Wasserman Schultz, D-Fla., and Rep. Mick Mulvaney, R-S.C.

On one side: Republicans want to delay President Barack Obama's health-care law and Democrats won't negotiate proposed changes to the law while talking about funding the government and whether to raise the debt ceiling.

Hours after the first government shutdown in 17 years began, the two lawmakers appeared Tuesday morning on CNBC.

(Read more: 800,000 out of work as US government shuts down)

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Here's the exchange during "Squawk Box" on the shutdown and the start of Obamacare's provision mandating that people buy health insurance through state exchanges or face fines:

"There are almost 750,000 uninsured and eligible South Carolinians today that can now sign up for the exchanges. They can sign-up for health-care coverage," said Wasserman Schultz, head of the Democratic National Committee. She went after Mulvaney in his own state.

"You can't sign up because the exchanges aren't ready yet," argued Mulvaney, a member of the House Committee on Financial Services.

Wasserman Schultz responded: "That's just completely untrue. There is an exchange up and running as we speak in South Carolina. You can go online sign-up for it."

"You're telling almost 2 million South Carolinians that as of January 1st who have a pre-existing conditions that they could still be dropped or denied coverage," she continued.

Mulvaney´╗┐ scoffed: "Two million people is half my state. That's absurd. Two million people is half my state. Those are absurd numbers."

"It's also absurd that you have shut the government down over a settled matter," Wasserman Schultz said.

In the beginning of the interview, Mulvaney´╗┐ explained why the GOP is fighting against Obamacare even though it doesn't have the votes. "At the end of the day good policy is good politics or else you might as well give up and go home."

He added, "If you're doing what you think is right, you hope the people will look favorably upon that."

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.