what the democrats are doing is taking something that has no effect on most people, and converting it into something that visibly affects a much larger percentage of their voting base, forcing them to react in ways they shouldn't have to.
they're taking something that people may abstractly oppose, and converting into something that concretely affects them, forcing them to react in a more visceral way.
the inevitable backlash does not come in the form of "ok, i support the wall, i guess" but in the form of "i don't fucking care about the wall, but i need this service, so build it already, if that's what you have to do to get the service to operate; the service is more important to me than the wall. and who is standing in the way? it's the congress? fuck the congress."