WASHINGTON—Since he became president, Donald Trump’s threats to sanction global trading partners sent tremors through business-oriented congressional Republicans worried about how potential retaliation from abroad could reverberate through the businesses and farms in their districts.

On Thursday, the rattle turned into an earthquake. The president’s announcement of plans to put barriers on steel and aluminum imports drew quick condemnation from GOP lawmakers who almost uniformly labeled the action a “tax” because of the potential...