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The stock market is not overvalued right now, but it's no bargain anymore, hedge fund giant Leon Cooperman told CNBC on Tuesday.
"By in large, we have not gotten into that speculative phase of the [bull] market," the chairman and CEO of Omega Advisors said in a "Squawk Box " interview. "As an investor, I think the market is reasonably valued. I have to kind of work hard and find stocks and macro themes."
With $9.5 billion in assets under management, Cooperman's Omega Advisors is up 26 percent this year compared with an increase of about 20 percent in the S&P 500, which closed Monday at 1,710.
Senate Majority Leader Harry Reid and Republican leader Mitch McConnell are said to be getting close to a deal to end the government shutdown—now in its 15th day—and increase the nation's borrowing limit into February. The Treasury's debt ceiling deadline is Thursday.
Later Tuesday, word came that House Republicans will propose their own bill to open the government and raise the debt ceiling, in return for various concessions related to Obamacare.
(Read more: Thursday debt deadline a 'soft date,' says Bowles)
The budget wrangling between Democrats and Republicans is a negative for the markets that should not be overlooked, stressed Cooperman, who described himself as socially liberal and fiscally conservative. "It's not an original comment by me, but I read somewhere, 'They closed the circus, but are still paying the clowns.' It's just disgraceful what's going on down there."
"The real issue in Washington is the long-term issue of whether we're receiving or achieving," he added.
"Our leaders have to agree on the appropriate maximum marginal tax rate on wealthy people, he said, "because once you agree on that number, that defines the revenue yield to the government. And then we have to size government to that revenue yield."
"[Warren] Buffett, which we all have enormous respect for, he would say and has said if you make over $1 million a year [it's] 35 percent. Maybe if you make over $5 million something close to 40 percent, " Cooperman said. "I'd sign right now on the dotted line for 40 percent."
Against this backdrop and projections for corporate earnings, Cooperman said, the stock market is fairly valued with the S&P 500 in the 1,650 to 1,750 range, adding that he doesn't see a bear market coming anytime soon. "Most bear markets are associated with recessions, " he said, "and we don't see a recession.
(Read more: Cooperman looks to go 10 for 10 again in 2013)
"China is getting a bit better, Europe is turning, and the U.S. is kind of grinding out 2 percent" economic growth, he said.
"What would make me negative [on stocks is] a 10 to 15 percent quick rise in the market, getting into that third phase of exuberance, which we're not at now—a view of a recession emerging, which we're not at now," Cooperman said. "There's much evidence that the economy is picking up a little momentum, not losing it."
He added that "very strong economic growth" would be a negative for stocks because that would bring the Fed into play. If we starting seeing 3 or 4 percent growth and tapering begins, then the markets will start to worry."
While low interest rates have helped investors, they hurt savers, he noted.
As for stock picks, Cooperman elaborated on a couple companies he chose as "best ideas " at this year's CNBC-Institutional Investor Delivering Alpha Conference in July.
His 10 picks were broken down into three categories, including "quality growth" where he chose Express Scripts, Qualcomm, and Thermo Fisher Scientific. His "phoenix from the ashes" picks were Qualicorp and SandRidge Energy. And his "growth with high-income situations" category, Arbor Realty Trust, Atlas Resource Partners, Chimera Investment, KKR Financial Holdings, and THL Credit rounded out his top picks.
On CNBC Tuesday, he said of Qualcomm: "We've been a little disappointed not in the fundamental performance but the stock price performance. We rotated out of Apple when Apple was trading in the $600s and put that money to work into Qualcomm. "
In his case for the stock, he added: "The S&P is over 15 times earnings. Qualcomm is 14 times earnings."
It has a "fortress balance sheet, ubiquitous in the smartphone game. Their chip is going into most all smart phones. We think it will probably grow—after a high growth rate this year—probably 10 percent going forward." He argued that it's "very reasonably valued, buying back $5 billion worth of stock, just very cheap."
Another Delivering Alpha pick Cooperman talked about on "Squawk" is SandRidge Energy. "We have a very positive view of SandRidge. A well-regarded hedge fund launched a proxy fight, replaced management."
"We think the news could get progressively better," he continued. "We think their acreage position in their production would justify a price probably 50 percent higher than it is presently."