Spicer apologised on Tuesday for "insensitive" remarks in which he asserted that unlike the Syrian regime, Adolf Hitler did not use chemical weapons.
Spicer said he knew that gas chambers were used to exterminate Jews during the Holocaust.
Spicer has since apologized for forgetting or ignoring that Hitler used poison gas to kill Jews and other minorities during World War Two.
Howard Stern is a longtime friend of President Donald Trump - but he's certainly no friend of Sean Spicer.
Speaking on his SiriusXM radio show Stern, 63, said: 'When I heard this, I was like, Trump's got to fire this guy.
"I've never understood these people being put in these specific positions of power, especially Sean Spicer and Kellyanne Conway", McCain said. From a professional level, I think it's disappointing because I think I let the president down.More news: Iran's President Rouhani: 'Iran will ask no soul's permission to build missiles'
Democratic Leader Nancy Pelosi released a statement following the press conference, saying that "Sean Spicer must be fired, and the President must immediately disavow his spokesman's statements".
The Anti-Defamation League responded by sending Spicer a letter that offered to teach him and other White House staffers about the atrocities of World War II.
After the hearing, Spicer said in a statement, "In no way was I trying to lessen the horrendous nature of the Holocaust".
Spicer apologized today for his comments during Tuesday's White House press briefing where he attempted to compare Assad's actions with those of Hitler. "So you have to, if you're Russian Federation, ask yourself is this a country that you and a regime that you want to align yourself with?" "The conflict in Syria is horrific, and Assad's regular use of chemical weapons, decades after they were banned, is abominable".
Perino was certainly sympathetic to Spicer and she told him, "I do think you're a little harder on yourself than you need to be".