We built the interstate highway system.
We built it with what were essentially defense funds, because that was the basis upon which it was sold. And it's falling to pieces even as we speak.
We sent rockets to the moon.
That was a long time ago.
Hell, China's got a wall.
Which didn't work. It was a halfway decent public works project, but inferior to doing something which would have benefited the people like building sewers or waterworks.
You can argue whether a wall is a good idea or not, but to say we can't build a wall is stupid beyond belief.
We can't build a wall in the same way that we can't run a nuclear reactor (PWRs on ships aside) safely. Once you account for malfeasance, you arrive at the conclusion that it cannot be done.