Carney said in a statement it would be "terrible to tell more than a million families across the country just a few days after Christmas that they're out of benefits," but how the extension is funded is not the greatest concern, The Hill reported Friday.
"The vehicle that they use to do that is less important than the fact that they do it," Carney said.
House Minority Leader Nancy Pelosi, D-Calif., said Thursday an extension of jobless benefits didn't have to be included in a proposed budget deal to win support from Democrats.
If the program is not funded before Dec. 28, some 1.3 million workers would lose their benefits.
Republicans suggested Friday the extension was not needed after the November jobless rate dropped to 7 percent, the lowest in three years. However, the White House noted the rate was still far higher than the 5.6 percent rate when president George W. Bush initiated the benefit.
Carney said Congress should act "as soon as possible" to raise the minimum wage. He wouldn't say whether President Barack Obama would use an executive order to raise the minimum wage for private-sector employees working on federal contracts, but he said the president is "always looking for ways to move the ball forward."
The president said Wednesday it was "well past the time" to raise the minimum wage.
A poll released last month found 75 percent of U.S. citizens supported raising the minimum wage to $9 an hour.