"I think that there's no question when you have eight years of one party in office, there are people who stay in government -- and continue to espouse the agenda of the previous administration," Spicer said.
"So I don't think it should come as any surprise there are people that burrowed into government during eight years of the last administration and may have believed in that agenda and may continue to seek it," he went on. "I don't think that should come as a surprise."
Spicer denied that the CIA was working to identify those people and remove them from office.
"That's not part of the CIA's mandate under any circumstances," he said.
But to some, "Deep State" has a far more insidious meaning than just government bureaucrats and Obama appointees still working in Washington.
Rep. Mike Kelly, a Pennsylvania Republican, alleged last weekend -- without evidence -- that Obama and his family were living in Washington in an attempt to undermine Trump's presidency.
"He's only there for one purpose and one purpose only and that is to run a shadow government that is totally going to upset the new agenda," Kelly said during an event in his home district.
Obama and his family rented a home in Washington after departing the White House so their youngest daughter could finish high school.
Kelly, in his remarks, alleged that Obama-era federal employees were rejecting the new administration's directives.
"The same people were there and they don't think the new owners or the new managers should be running the ship," he said.
Rep. Thomas Massie, R-Kentucky, told CNN's Kate Bolduan last month he disagreed with "a lot of people here in Washington and maybe some supporters of Trump who say that this is an effort by the Obama administration to undermine the Trump administration."
"I'm worried it's something deeper than that," Massie said. "I'm concerned that it's an effort on those who want a provocation with Russia or other countries to sort of push the president in the direction. So I don't think it's Trump vs. Obama, I think it's really the Deep State vs. the president, the duly elected president."
The phrase, as it's used by Massie, was popularized in Turkey. In 2012, a CNN report described it as a "term many Turks use to refer to alleged criminal networks within security forces and the government bureaucracy." It was first used in The New York Times in reference to Turkey in a 1997 article that defined it as "a set of obscure forces that seem to function beyond the reach of the law."
It has since been used to describe unelected but influential members of groups including the bureaucracy or the military in countries like Egypt and Russia, and increasingly in some circles, the United States.