In a cruel twist of fate, guess who the biggest losers are when a country imposes tariffs on imports? Its own exporters. The reason why seems to be two-fold. Firstly, the tariffs on imports take cash away from foreign countries to buy exports. Secondly, such tariffs often lead to retaliations, which then shrink the size of exports (e.g. what is happening to Harley Davidson right now). The link has been well understood by economists for almost a century, but new research shows it concretely in trade flows. Overall, the trade balance does tend to improve, but exporters suffer significantly.
FINSUM: The problem is that trade wars are almost a zero sum game. That said, the US has a better bargaining position than usual in this one.