He added, "There's not going to be any opportunity to cut Pentagon spending in any serious way, if you don't go over the 'sequester' cliff."
Paul McCulley, former Pimco managing director, agreed with Dean. "Going over the 'sequester cliff' may be the only way to get the defense budget clearly on the table," he said on "Squawk Box" Monday. "[It] needs to be on the table."
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McCulley, now chairman of the Global Interdependence Center, also predicted that triggering the spending cuts would not be a disaster for the stock market. "I think we'd have some skittishness in the marketplace. But it doesn't fundamentally change matters."
The across-the-board spending cuts are designed to force savings of $1.2 trillion through 2021. That means for this year, and every year after that, about $55 billion would be cut from defense spending and about $55 billion of reductions would come from non-defense spending.
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President Barack Obama and Republicans leaders are working on a package to replace the automatic cuts. But the president wants more revenue by closing tax loopholes, and the GOP wants to talk spending cuts since the compromise last month to avoid "fiscal cliff" was mostly tax increases.
Dean advocated going over the "sequester cliff" now, just as he had pushed for going off the "fiscal cliff" at the beginning of the year.
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He said, "I don't think [tax rates] should go higher, on the high end," which was defined in the January deal as individuals making more than $400,000. "[But] I've always said 'if you want Bill Clinton's economy, you've got to pay Bill Clinton's taxes.'"
"Republicans won the fight in January they just don't know it," Dean said. "Washington is upside down."
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"The Republicans won an enormous victory. They stabilized taxes for middle class people at the Bush tax rates for everybody below $400,000."
He argued, "We did a lousy job in January on the tax side … I think it's better to go over the 'sequester' cliff then do a lousy job in February."
—By CNBC's Matthew J. Belvedere; Follow him on Twitter