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Obama has chance to be 'Clintonesque': Policy pro

'Brinkmanship' constrains US credit rating: Pro

With the latest federal debt crisis over for now, what does the U.S. need to do to get back its AAA credit rating from Standard & Poor's?

The short answer: Start by stopping the "brinkmanship," S&P lead analyst on U.S. sovereign ratings Marie Cavanaugh told CNBC Thursday—hours after President Barack Obama signed the last-minute congressional deal to extend debt ceiling until Feb. 7 and reopen the government by approving funding until Jan. 15.

"The president has a chance to be downright Clintonesque here," said Chuck Gabriel, managing director at Capital Alpha Partners, a research and policy advisory firm. "He has Republicans right where he wants them. He has all the leverage."

U.S. stock index futures were lower in pre-market trading Thursday, after a strong rally Wednesday on indications that a deal would get done.

(Read more: Markets ready to shift focus back to economy, earnings)

Going forward, House Speaker John Boehner has named a slate of negotiators led by Budget Committee Chairman Paul Ryan to craft a budget that "addresses the drivers of our national debt and deficits, and helps strengthen our economy and create new jobs."

"Democrats looking at this new budget committee might be satisfied with just a couple of years of partial relief on the sequester and forget about a Grand Bargain," Gabriel said in a "Squawk Box" interview.

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Cavanaugh said the government shutdown has clipped at least 0.6 percent off annualized fourth-quarter 2013 gross domestic product growth or, in other words, has taken $24 billion out of the economy.

"There are many credit strengths in the United States," she continued. "But the constraints in our opinion are this brinkmanship which relates to the very unusual budgeting strategy where by the spending decisions and the funding decisions are separate. That's not the case for most governments."

"This [stock] market has been fed since early 2009 by climbing little walls of worry," Gabriel of Capital Alpha Partners argued. "If we get continuing resolutions just to fund the government through the end of this election cycle, that would be okay."

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But the U.S. debt is still "fairly high," Cavanaugh said. "It's actually stabilizing in our opinion over the next few years, but then we'll begin to edge upward without additional fiscal measures."

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