US consumers are first and foremost US workers first -- and only consumers in as much as they have a job and they make enough to pay rent, consume, etc.
So while they might not get cheap global shit as easily, they'll be able to get jobs easier...
Then don't impose a tariff on steel, impose a tariff on consumer products. It's an instrument of economic policy, not a binary all-or-nothing choice.
However, this policy is being sold as a way to help US manufacturers and that's not quite the same thing. The benefits could easily go to other imports with weaker tariffs. This coupled with the problem of hurting down stream US manufacturers means that the only benefit is hedging against a Chinese monopoly and not the direct benefits that are usually talked about.