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Few of those coming to his defense, however, are from outside the administration or the president's family.
Republican National Committee Chairwoman Ronna Romney McDaniel told Fox News that the president "acted like a human, and he pushed back."
McDaniel did not specifically defend Trump's calling Brzezinski "low I.Q." and Scarborough "psycho" or the president's alleging that Brzezinski was "bleeding badly from a face-lift."
But the GOP chairwoman said the "Morning Joe" hosts on MSNBC have been insulting to the president.
"They've said he has dementia. They've said he's stupid. They've called him a goon. They've called him a thug. They've said he's mentally ill. They've said he's an embarrassment," she said. "This is the type of thing they say day after day for two hours on their network where they control the narrative and ... today, the president acted like a human, and he pushed back."
McDaniel added, "We can have a discussion about who's right or wrong, but at the end of the day, we have to focus on the American people and who ... sent us here to lead and make their lives better and that's what Republicans are going to do every day," she said.
Fox News anchor Julie Banderas challenged this argument by pointing to the reaction of former President Obama when insults were leveled at him. "They've called him every name in the book but you didn't see him lash out," Banderas said.
McDaniel, who is the granddaughter of former Michigan Gov. George Romney and niece of former presidential candidate and Massachusetts Gov. Mitt Romney, replied that political vitriol can hit home.
"I've been a daughter of a candidate and I've been a niece of a candidate ... it's personal sometimes," she said.
Another defense of Trump came from Fox News anchor Sean Hannity, who is a public supporter and sometime adviser of Trump. During his radio show broadcast on Thursday, Hannity acknowledged reservations about the president's "Morning Joe" tweets, but he repeatedly slammed the news media and said Trump should continue to use social media to speak "directly to the American people."
"I'm not sure I would have advised him to tweet out what he did to Mika and Joe today," Hannity said. "I think that's one of the 10 percent of tweets that end up in the mistake column in my opinion."
Hannity added, “My message to the White House would be this: Ignore these people in the media. They don’t like you. They never liked you. They don’t support you."
His guest on the show, former House Speaker and fellow Trump supporter Newt Gingrich, agreed with Hannity.
Inside the Trump administration, deputy press secretary Sarah Huckabee Sanders spent much of the White House briefing on Thursday defending Trump's decision to, as she put it, "fight fire with fire."
"I think that the president is pushing back against people who attack him day after day after day," she said.
"The president normally does not draw first blood. He is a counter-puncher," Conway said. "I endorse the president’s right to fight back when he is being mercilessly attacked and when the airwaves are filled with raw sewage about him and his fitness for office."
Conway did not say, however, whether she supported Trump's "attacks" against the "Morning Joe" hosts.
"I didn’t say I endorsed his attacks; I never said that," Conway said to Stephanopoulos.
As for the president's family, first Lady Melania Trump's spokeswoman, Stephanie Grisham, issued a statement Thursday. Later in the day, Grisham said the statement should be read not as a direct defense of or reaction to the president's tweets that morning but as a reiteration of previous statements by the first lady.
"As first lady has stated publicly ... when her husband gets attacked, he will punch back 10 times harder," Grisham said.