The loss of benefits could spur former recipients to either drop out of the labor force or accept jobs they previously would not have considered. Some economists estimate this could lower the current unemployment rate of 7.3 percent by as much as half a percentage point.

"The lapsing of the program could lower the unemployment rate by perhaps 0.25-0.50 percentage point, with much of the effect coming through reduced labor force participation, rather than increased employment," said Michael Feroli, an economist at JPMorgan in New York.

Editor’s Note: Retired Americans Slammed by Obama’s Redistribution Plans

To receive jobless benefits, Americans are required to be actively looking for work. That is also a key factor that defines who is unemployed, as opposed to those who have dropped out of the labor force.

Emergency jobless benefits for 1.3 million long-term unemployed people are set to run out on Jan. 1 unless the U.S. Congress agrees on an extension.

The National Employment Law Project, a New York-based advocacy group, estimates that about 850,000 people will run out of state unemployment benefits in the first quarter of 2014, with no access to emergency benefits if lawmakers do not act.

The emergency unemployment compensation program was introduced in 2008 during the depths of recession, and has been extended every year since then. It has paid out more than $225 billion to cushion the long-term unemployed as the economy struggled to heal from the recession.

President Barack Obama and his fellow Democrats want to include an extension of the program in any budget deal hammered out by a bipartisan panel. A negotiating panel has been given a Dec. 13 deadline to reach a deal to fund the government.

With little time left, and opposition to an extension among some Republicans, analysts say it appears likely the emergency benefits will expire as scheduled on Jan. 1.

HEADACHE FOR FED

The U.S. jobless rate has dropped 2.7 percentage points from a peak of 10 percent in October 2009, though some of the decline has been due to Americans giving up the search for work.

Goldman Sachs expects an expiration of emergency benefits would reduce the jobless rate by between 0.1 and 0.2 percentage point in early 2014.

"If, hypothetically, all workers receiving emergency unemployment benefits dropped out of the labor force once benefits expired, this would result in a 0.8 percentage point decline in the unemployment rate," said Alec Phillips, an economist at Goldman Sachs in Washington.

"If all of these workers became employed, the resulting unemployment rate would be only slightly lower. However ... we would expect the actual effect on the unemployment rate to be significantly less dramatic than either of these hypotheticals."

Should the unemployment rate drop because former recipients of jobless benefits have dropped out of the labor force, that could pose problems for the Federal Reserve, which has put the unemployment rate at the center of monetary policy.

The Fed has said it will hold interest rates near zero at least until the jobless rate drops to 6.5 percent. But if a big part of the decline reflects people dropping out of the labor force, that could be seen as a sign of weakness, not strength.

"Such a fall in the unemployment and participation rates could create some tricky choices for Fed policymakers as they assess the health of the labor market," said JPMorgan's Feroli.

Not only will the expiration of emergency benefits affect the unemployment rate, it could also hit consumer spending and ultimately economic growth in the first quarter of 2014.

"The program currently pays out benefits at around a $20- 25 billion annual rate," said Feroli. "Should that flow dry up, consumer spending could take a hit in the first quarter, perhaps subtracting around 0.4 percentage point from annualized real GDP growth in that quarter."

Editor’s Note: Retired Americans Slammed by Obama’s Redistribution Plans