He cited the recent example of Trump blaming generals for the loss of Senior Chief Petty Officer William "Ryan" Owens during a covert mission in Yemen. ("They lost Ryan," Trump said in an interview with Fox News that aired Tuesday).

"That's not how George W. Bush, or Barack Obama, or Bill Clinton, or George Herbert Walker Bush, or Ronald Reagan talked about the military," Schmidt said. "He was a president who served in turbulent times and was controversial, but as is always the case -- when a president has distance from their presidency, voters look at them and are much more likely to see their virtues than their flaws."

Trump tempered his tone -- at least temporarily -- with a strong performance at Tuesday's joint address to Congress. The emotional high point of his speech came when he spoke directly to Owens' wife, Carryn, who watched the speech from the first lady's box.

He also spoke in more measured terms about race and the need for the country to unify even as he maintained hardline positions on issues such as building a wall along the US border with Mexico and repealing and replacing Obamacare.

On the news interview circuit this week, Bush has been peppered with questions about Trump's controversial actions on immigration and his targeted travel ban (which was halted by the federal courts).