The fashionable despair of America fixing its trade mess is a mistake.
For example, the standard objection to taking a stick to America's trade imbalance by levying a tariff is that our trading partners would just shrug it off by increasing subsidies to their exporters. (They do something similar to this already: China, for example, is constantly adjusting its export subsidies to protect its positions in foreign markets.) This would, supposedly, force us into an endless game of matching these moves on a country-by-country, industry-by-industry, and even product-by-product basis.
However, retaliatory subsidies by our trading partners would be restrained by the fact that they would be very expensive in the face of an American tariff. Right now, these subsidies are relatively affordable only because they don't have to climb an American tariff wall. But if they did, their cost would increase dramatically. Escalation is a game two can play, and no, this wouldn't lead to a trade war.
Currency manipulation is probably the only subsidy that is affordable over prolonged periods of time (and even then problematic in the end), as it involves buying foreign assets and debt, thus accumulating wealth rather than just expenditures. But other subsidies amount to a giveaway from the exporting to the importing nation.
While this doesn't prevent them absolutely, it does tend to set a limit. This is all we need, especially as we have no hope of eliminating or countervailing all foreign subsidies no matter what we do, tariff or no tariff.
The same goes for the objection that our trading partners would just devalue their currencies. We can end foreign currency manipulation at any time simply by restricting or taxing foreigners' ability to lend us debt and buy our assets. We would need to raise our own savings rate if we did this (or face rising interest rates), but we need to do this anyway.
So it's an utter mistake to think America is this big helpless giant with respect to its trade problems. The solutions are out there if we would but avail ourselves of them.