First, I assume you are talking about the land border wall here. If you wanted to truly seal off the US-Mexico border with a wall, you would have to build a wall along the beaches of California, Texas, Louisiana, Mississippi, Alabama and Florida, too.
Secondly, it isn't clear from your question whether you are asking about the construction cost or the operating cost. While I speculate that you meant to ask about the construction cost, the lion's share of the cost will be maintenance and operation.
For that, some back-of-the-envelope calculation will result in dramatically large numbers.
I am assuming that this wall would be secured similar to the wall between Germany and East Germany in the 1980s. That wall was far from impenetrable, but we can probably call it fairly good in terms of security (not that any wall is ever "good" in a moral sense). In some areas, such as between San Diego and Tijuana, the US-Mexico border is designed very similar to the East German wall.
Of course, the East German border wall was very short (~300 km, I believe, plus another ~180km around Berlin), but also maintained by a much smaller country.
The East German border wall was staggeringly expensive, and some people argue that it was a major factor in East Germany's eventual bankruptcy.
A wall like that requires watch towers approximately a km apart, give or take (in some cases, they were spaced much closer together). Each tower was manned by approximately 3 guards (soldiers in the case of East Germany) at a time, operating in shifts 24/7. So after taking weekends, vacations, training, sick days etc. into account, you will need approximately 12 or so full-time guards per mile, probably more than that. Keep in mind that this number is based on a country with no qualms about using landmines, automated guns, and shoot-to-kill orders. Hopefully, any wall in the US would be more humane. That would drive up your manpower requirements.
You also need probably roughly an equal number of support personnel, doing anything from logistics to/from all those towers, vehicle maintenance, human resources, management, etc.
Note that these guards cannot actually be replaced with technology. Cameras, drones etc. don't do much good when the nearest border patrol agent is an hour's drive away!
Translating that to the US-Mexico land border of 3145 km, that means you need nearly 80000 border guards and support. Just for the land border to Mexico - not even including the coasts or the border with Canada. For comparison: the whole Border Patrol today only has about 20,000 people - and that's for all borders, coastlines, airports, and a lot of inland stuff.
That would be roughly half the size of the US Marine Corps.
On top of that, the wall is not a "build it and forget it" construction project; it needs continuous ongoing construction work. That's why the vast majority of Trump's wall replaced existing sections, and added only a few new miles to the wall.