He did promise it. That was a big part of the sales pitch. No wall is like getting that 600hp muscle car only to find someone stuffed in a Yugo engine instead.
Trump will either build that wall, or he will not get a second term, and even worse from his perspective, he will go down in History as a failure. I think Ann is tweaking his nose to rouse some anger, and give him a little fire in the belly.
I'm thinking that he could perhaps issue orders that the US Army will immediately set up camps and patrols near known border crossing areas.
The reasoning behind this is to get those troops and their families bitching about the government not doing anything to solve the problem other than have them doing this drudge work.
Get enough people bitching (and their are troops from all the different states) and you can perhaps start getting pressure applied to congress to "build the damn wall!"
Treat it like it's a serious enough issue to call for military intervention, and perhaps people will start looking at it seriously.
In any case, it is within his powers to do this, and it should result in pressure on Congress.