"Christmas-time is no time for Congress to tell more than 1 million of these Americans that they have lost this unemployment insurance," Obama said in a speech on Wednesday. "(That's) what will happen if Congress does not act before they leave on their holiday vacation."
The White House points out that if benefits expire, U.S. GDP could fall next year by 0.2 to 0.4 of a percentage point, according to the Congressional Budget Office and a J.P. Morgan Chase(JPM) economist.
The report also suggests the economy isn't strong enough to end benefits.
Republicans had been cool to the idea of extending benefits, saying in memos that the program has already cost $252 billion through July.
But, on Thursday, House Speaker John Boehner suggested he was open to an extension.
"If the President has a plan for extending unemployment, I'll take a look at it," Boehner said.
The program was first signed into law in June 2008 by President George W. Bush, when the unemployment rate was 5.6% and the average duration of jobless insurance was 17.1 weeks.
The unemployment rate climbed to more than 10% at the height of the Great Recession in 2009, and the government extended the federal benefits to jobless Americans whose state unemployment insurance had run out.
Federal unemployment insurance benefits kick in after a person's state benefits run out, and range between 14 to 47 weeks, depending on the state a person lives.
Only residents in Nevada and Illinois have access to the maximum 47 weeks, according to the National Employment Law Project, an advocacy group. Most states have cut back unemployment benefits, as the labor market has improved.
"As lawmakers prepare to head home to be with their families during the holiday recess, they must not turn their backs on millions of families struggling with long-term unemployment and a weak labor market," said Christine Owens, executive director of the National Employment Law Project in a statement.
Labor Sec. responds to low-wage job growth
The cost to extend the federal benefits by another year is about $26 billion, according to the Congressional Budget Office.
-- CNN's Lisa Desjardins contributed to this report.