The large number of long-term unemployed — those who have been out of work at least six months — constitutes the economy's "most serious problem" now, Alan Krueger, former chairman of President Barack Obama's Council of Economic Advisers told CNBC.

The long-term unemployed accounted for 3.8 million of the 10.5 million people who were jobless in February. A recent study by Krueger, now a professor at Princeton University, and two other economists there showed that only 11 percent of the unemployed find a new job within a year.

"The longer people are unemployed, the more challenges they face," Krueger told CNBC.

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"Employers are less likely to call them in for interviews. They grow discouraged. Their skills grow obsolete. They become more isolated, more disengaged."

Krueger said the long-term unemployed need help from both monetary and fiscal policy. While monetary policy can't focus on them directly, Federal Reserve stimulus has boosted the labor market in general, he said.

Krueger recommends tax breaks to encourage employers to hire those who have been out of work a long time. Many employers are biased against them, because the employers "figure there's a reason why these people have been passed over," Krueger said.

Some economists turned optimistic about the overall labor market after the government reported that non-farm payrolls rose 175,000 in February.

"It's a very encouraging report, indicating that we've mostly seen weather disruptions," Morgan Stanley economist Ted Wieseman told The Wall Street Journal.

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