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Lehman a 'kindergarten show' next to any default

Stock market traders and investors don't believe the fight over the debt ceiling will result in a U.S. default, closely followed value investor Bill Miller told CNBC on Tuesday, hours after the first government shutdown in 17 years.

But if for some reason the federal government didn't pay the interest on the debt, he warned, that "would make Lehman Brothers look like a kindergarten show."

"The real issue is the debt ceiling, not the government shutdown," Miller said in a "Squawk Box" interview. The Treasury has set Oct. 17 as the deadline for the nation's borrowing authority to be increased.

(Read more: Washington hasbecome 'Land of Oz': Citi chief economist)

Miller—portfolio manager of the Legg Mason Opportunity Trust fund—pointed out that the debt ceiling fight in the summer of 2011 resulted in a downgrade of the U.S. by Standard & Poor's. "But that was in conjunction with the European crisis. So we don't have that European crisis now, and there's virtually no chance we'll have any kind of default."

(Read more: S&P to hold fire on US credit downgrade—for now)

The Legg Mason Opportunity Trust fund returned nearly 40 percent in 2012.

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

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