The administration announced Friday an agreement with Mexico that sees the country take tougher measures on illegal immigration in exchange for the U.S. dropping plans to impose tariffs on imports.
Trump fumed on Twitter Monday morning over a New York Times report that the deal included a range of actions that Mexico already promised to take in prior negotiations with the administration over the past several months.
Scarborough said Trump's statements are more "ground noise" intended to distract his base, while Meacham compared the president to a "Mary Poppins" character.
"We may look back at the Trump presidency as the presidency of Admiral Boom. Remember the guy who lived next door to Mary Poppins who had the ship on top of the house? And he thought he was still in the Navy and so he'd fire the cannon off at cocktail hour; everybody sort of humored him," Meacham said.
"I continue to think foreign leaders must look at this presidency in the way we used to look at particularly unstable regimes. ... Why would any foreign power take him at face value?" he asked.
Scarborough said Trump is taking a "shortsighted" view with his trade policies, including tariffs on China and Mexico.
"The president wants the big headline; he wants the all-caps tweet, but at the end of the day it's working-class Americans, middle-class Americans and farmers who will feel the pinch of these policies," he said on "Morning Joe."