When Mr. Trump fires off a tweet, the president gets visibly excited when he comes up with a message he believes will go over well with his base — he peers over his phone with a “watch this” expression, according to two people who have observed such a process.

The wall rhyme appears to fit into that same bull’s-eye category. The White House press office did not respond to a request for comment about the origin of Mr. Trump’s latest catch phrase on Wednesday. But a senior aide to the president said that Mr. Trump came up with it himself, and credited the new slogan to his “marketing genius.”

There are a few hitches: Mr. Trump’s rhyming sales pitch that a border wall will reduce crime is not credible, and the facts he uses to bolster his claims are often correctable.

First, despite the president’s repeated claims, construction has not yet started on the border wall: The “under construction now” in his morning tweet needs more context. Customs and Border Protection has begun or completed several projects to replace old fencing with new barriers, but no additional miles of wall have been added yet. Construction to build a new levee wall system in Texas is scheduled to begin in February, the first extension of existing barriers.

Second, Mr. Trump’s rhyme that a wall will lead to falling crime rates may be catchy, but it’s at odds with what data shows about the influence immigration has on crime.