Democrats on Friday said that while they were encouraged by an October jobs report showing about 204,000 jobs were created in October, the numbers would have been better without the government shutdown. Some Republicans, meanwhile, suggested the report vindicated their shutdown strategy.

"Consider how much stronger job growth and the economy could be without the Republican government shutdown and debt limit brinksmanship," House Minority Leader Nancy Pelosi (D-Calif.) said in a statement.

Jason Furman, chairman of the White House Council of Economic Advisers, pointed to progress leading up to the shutdown and said it was thwarted.

"The upward revisions to job growth in August and September, combined with solid third quarter GDP growth reported yesterday, suggest that the economy was gaining traction in the months leading up to the government shutdown," Furman wrote. "There should be no debate that the shutdown and debt limit brinksmanship inflicted unnecessary damage on the economy in October."

Senate Majority Leader Harry Reid (D-Nev.) has said that the shutdown cost the country between 125,000 and 250,000 jobs, citing the White House's estimates.

Some Republicans, though, pointed to the stronger-than-expected job growth (the economy was expected to add only about 120,000 jobs) as proof that the government shutdown didn't do significant damage to the U.S. economy.

The 204,000 preliminary number -- which might be later revised -- is the third-biggest for job growth this year.

A top aide to Sen. Ted Cruz (R-Tex.), who led the Defund Obamacare movement that drew a hard line on government funding, also linked to the CNN report that suggested the shutdown had little impact on jobs.