The estimated cost for shutting down the government for a day is $100 million.
Obama signed the order on Friday closing all federal executive departments and agencies on Christmas Eve and making the day a holiday for their workers.
The decision to grant federal employees a four-day weekend came after 28,257 people signed an online petition on the White House "We the People" website requesting it.
"Federal employees have had a pay freeze for the past several years and the pay and benefits for the federal workforce have been under serious attack during the national elections held this year," said the petition, which was started on Dec. 1.
"Giving federal employees an extra holiday on December 24th, 2012 would be a good gesture to improve morale of the federal workforce," it said.
Some federal workers have had their pay frozen since 2009. In 2010, Obama announced a blanket two-year pay freeze for all civilian federal workers, citing the government's budget deficit. The move was expected to save the government $28 billion over five years.
The freeze, which began on Jan. 1, 2011, was set to expire Dec. 31. But on Friday the president formally extended it through March 27. Obama and Congress had agreed in the fall to continue the pay freeze through the end of the current temporary federal spending legislation, which expires on that date.
Monday wasn't the first time that federal workers were given time off on Christmas Eve when it did not fall on a weekend, according to the petition. Obama gave federal workers a half-day off in 2009. President George W. Bush gave a half-day holiday in 2002, and full days in 2001, 2003, 2007 and 2008.
Aside from Christmas Eve, federal workers received 10 paid holidays in 2012, according to the Office of Personnel Management.
Workers who already had planned to use annual leave to take off Christmas Eve will not be charged for the day off, according to a memo for executive agencies from John Berry, director of the Office of Personnel Management.
Representatives of the U.S. Office of Personnel Management and the White House Office of Management and Budget did not immediately respond to requests for comment Monday.
A rival petition on the White House website asked Obama only to allow federal workers to use some of their "generous amount" of annual leave on Christmas Eve.
"We do not need to be given another holiday when so many people are looking for work," read the petition, purported to be from federal workers. That petition, created on Dec. 18, had 487 signatures.
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