John Dickerson: Kelly's speech touched on the fear of "split in America"

White House chief of staff Gen. John Kelly's Thursday speech touched on a broader, general fear that "political fights are now permanent and there has been a split in America that is forgetting our common humanity," CBS News chief Washington correspondent and "Face the Nation" host John Dickerson said. 

The only way out of the "constant combat," Dickerson said, is "if someone shows restraint or extends a hand to the other side in the name of that sacred sacrifice that Mr. Kelly was talking about today." 

Kelly's extraordinary -- and unexpected -- statement Thursday came during an emotional week in Washington, which began Monday when President Trump claimed Monday that other presidents did not call the families of fallen soldiers. 

Speaking to Fox News Radio's Brian Killmeade on Tuesday, Mr. Trump said, "I mean you can ask General Kelly, did he get a call from Obama?" referring to Kelly's son Robert, who was killed in Afghanistan in 2010. Kelly, who has been reluctant to speak about his son, did confirm Thursday that he did not get a call from former President Obama.  

Later on Tuesday, U.S. Rep. Frederica Wilson (D-Miami) characterized Mr. Trump's remarks to Army Sgt. La David Johnson's widow, Myeshia Johnson, as "disrespectful." Myeshia Johnson was on her way to the airport to greet the remains of her husband when she received the call from the commander-in-chief, CBS Miami reported. Wilson said she was in the car where the phone call was received.

On Thursday, Kelly said he was "stunned" to find out that Wilson had listened to the phone call.

"I was stunned when I came to work yesterday morning, and brokenhearted at what I saw a member of Congress doing," Kelly said, "a member of Congress who listened in on a phone call from the President of the United States to a young wife, and in his way, tried to express that opinion: that he's a brave man, a fallen hero."

Kelly's unexpected appearance in the White House briefing room was deeply personal and political and expressed real regret that this debate had crossed into what he considered sacred ground. 

"Everything is a chance to score a point," CBS News' Dickerson said. "And thankfully, Secretary Mattis has said, the military has not been corroded by that constant combat. But that may have now changed because this recent back-and-forth touches on this most-sacred part of public life -- a commitment by men and women to offer their life for their country. No one wants to cheapen that."

"But now we're in the third round or so of this fight in which each side is looking for the devastating blow to score against the other," Dickerson said. "The only way that these get reset is if someone shows restraint or extends a hand to the other side in the name of that sacred sacrifice that Mr. Kelly was talking about today."