On the conservative side, Trump adviser Kellyanne Conway, dismisses claims that Bannon has connection to white nationalist viewpoints, telling reporters, "I'm personally offended that you think I would manage a campaign where that would be one of the going philosophies". The site has a history of publishing incendiary and divisive stories, many of which are outright anti-Semitic, misogynist and racist.
Internal deliberations about staffing come a day after Trump made overtures to warring Republican circles by appointing Bannon and RNC Chairman Reince Priebus as his White House chief of staff.
The site was a virulent pro-Trump voice throughout the campaign. White nationalists of the so-called alt-right love it. In July, Bannon described Breitbart as "the platform for the alt-right".
Priebus on Monday said "That wasn't his writing", referring to Bannon, although he did not specify which, if any were Bannon's work.
"There should be no sugarcoating the truth here: Donald Trump just invited a white nationalist into the highest reaches of the government", said Democratic Senator Jeff Merkley, who called on Trump to rescind the choice.
The appointment of the Breitbart chief has drawn concern from Congress and nonprofit organizations, with the Anti-Defamation League saying Sunday is "strongly opposes" the Bannon pick.
Trump on Sunday afternoon named Bannon - the controversial conservative firebrand executive editor of the Breitbart website and CEO of Trump's presidential campaign - as chief strategist and counselor to the president. "It's for this reason that Bannon is so beloved by the white-supremacist movement in the US, and they are now celebrating his appointment".
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John Weaver, a Republican who worked for Republican John Kasich's campaign tweeted the "fascist extreme right is represented footsteps from the Oval Office".
"The president-elect has to be able to select his best team", House Majority Leader Kevin McCarthy (R-Calif.) said Monday to reporters asking him whether House Republicans were comfortable with Trump choosing Bannon.
Democrats also tried to sound the alarm on the growing influence of Breitbart over Trump's campaign.
That Bannon would have the ear of the most powerful leader in the world has critics on the left and the right alarmed. In the complaint obtained by Politico, Bannon's then-wife said he "pulled at her neck and wrist" and smashed the phone when she tried to call the police after a dispute over money. The litany of Breitbart's horrific statements is appalling: calling a prominent political commentator a 'renegade Jew, ' insinuating that African Americans and immigrants are inherently criminal, suggesting that women who suffer harassment should stay silent and promoting the Confederate flag right after the Charleston shooting. An increase in transgender hate crimes was also reported.
The Trump transition team and Breitbart did not immediately respond to requests for comment.
President Barack Obama, who Trump will succeed on January 20, declined to wade into the controversy at a White House news conference, saying it would "not be appropriate" for him to comment on Trump's appointments. For millions of people, including families in my district, Trump's election means they are now living under a shroud of fear.
"Bannon and Breitbart have made a business of attacking people based on their race and religion", said McMullin, who is Mormon.