The scene is said to have played out in the Oval Office in the early weeks of Donald Trump's presidency.
The president will come face to face with illegal immigrants during his address to Congress.
Trump's senior policy advisor, Stephen Miller, is hindering progress on an immigration deal, GOP Senator Lindsey Graham told reporters.
In 2003, Miller wrote that Osama bin Laden “would feel very welcome” at his high school in Santa Monica, California, after school administrators invited a Muslim cleric to speak on Islam.
The policy adviser became heated when discussing Donald Trump.
The president suggested Miller had "destroyed" Tapper during the interview.
“I get it. There’s one viewer that you care about right now and you're being obsequious and you’re being a factotum in order to please him, OK,” Tapper said.
Miller had not previously been identified in documents related to the investigation by special prosecutor Robert Mueller.
The president’s agenda is helping African-American and Hispanic workers, according to Miller.
Jim Acosta quoted the most famous couplet from Emma Lazarus’s 1883 poem The New Colossus etched on the Statue of Liberty in his argument with Stephen Miller.
Policy aide continues the administration's attacks on the judiciary, declines to detail next legal steps.