Many smaller countries’ exports have faced 10 percent tariffs since the president first announced, then suspended, an initial wave of policies in April. Others have staved off eye-watering rates after brokering deals with the United States that set their tariffs generally between 15 and 20 percent.

Advisers used tough tactics to bring desired trade deals to the president, but key details in many remain unfinished.

Trading partners might not make good on their commitments, tariffs could drive up inflation and stymie growth, and courts could rule against the president’s ad hoc levies.