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Alan Krueger, Obama’s chief economic adviser, said the report “provides further evidence that the economy is continuing to heal from the worst economic downturn since the Great Depression.”

Campaigning in New Hampshire for Obama’s job, former Pennsylvania Sen. Rick Santorum claimed credit for Republicans, suggesting the gains were tied to voter optimism that a Republican would take the White House.

“There’s a lot of concern still,” added Santorum, who finished in a virtual tie with Mitt Romney in the Iowa caucuses earlier this week. Another candidate, former House Speaker Newt Gingrich, dismissed the job gains as inadequate.

The report painted a picture of a broadly improving job market. Average hourly pay rose, providing people more money to spend. The average workweek lengthened, a sign that business is picking up and companies may soon need to hire.

The private sector added 212,000 jobs in December. Those gains were offset by 12,000 layoffs by governments.

Hiring increased across industries. Manufacturing added 23,000 jobs, as did the health care industry. Transportation and warehousing added 50,000 jobs. Retailers added 28,000. Even the beleaguered construction industry added 17,000.

Economists cautioned that some of the gains reflected temporary hiring for the holiday season. The government adjusts the figures to try to account for those seasonal factors, but doesn’t always get it exactly right.

The gains in transportation and warehousing, for example, reflected a strong increase in hiring for couriers and messengers. That could be because of the jump in online shopping over the holidays, the Labor Department said.

And the economy still faces many challenges, including a likely recession in Europe exacerbated by the debt crisis there. That could drag on the U.S. stock market, making U.S. consumers feel poorer and weighing on their spending.

In a reminder of the threat, U.S. stocks, which had appeared poised for a higher open, sank in morning trading. The Dow Jones industrial average was down 19 points. Analysts blamed a spike in borrowing costs for Italy, an ominous sign for the debt crisis.

“While December’s data represent good news, there is no guarantee that January will follow a similar path,” said Joshua Shapiro, chief economist at MFR Inc., in a note to clients.

The nation’s work force, which includes both people working and those searching for jobs, shrank slightly in December and doesn’t look much different from last spring.

That is a concern because a strengthening job market normally draws more applicants. And if more Americans are motivated to start looking for work, the unemployment rate could jump again.

The government only counts people as unemployed if they are actively searching for jobs. Discouraged workers who have given up on looking are not included in the rate.

And some of those who are counted as employed are working part-time, but would rather have full-time work.

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