Final answer:
In response to an invasion, the U.S. would likely take military action, which could include a declaration of war based on historical precedent. This action would be measured, deliberate, and substantial, reflecting past responses to acts of aggression against the United States.
Step-by-step explanation:
Given a hypothetical scenario where soldiers from another nation have invaded the United States, the appropriate response according to the United States' historical actions would likely involve military action and possibly a declaration of war. This is evidenced by the U.S. response to historical events such as the attack on Pearl Harbor during World War II, and the response to the unprovoked aggression of other nations. The United States typically has not ignored such acts but has responded with measures ranging from demanding international intervention, preparing for war, or directly declaring war. In contrast to the isolationist approaches the U.S. sometimes adopted prior to World War II, where intervention was avoided even when US interests were attacked, the modern response to an invasion on U.S. soil would be decisive.
Examining past wars, such as World War I, shows that the U.S.'s entry into the war involved not just sending supplies and economic aid but eventually escalated to sending troops and establishing an independent American military presence, as was the case under General Pershing's command. The decision to enter war often also leads to a rapid expansion of the military and a mobilization of economic and human resources. Hence, if an invasion occurred, it is highly likely that the U.S. would respond with strong military action, potentially up to a declaration of war as a final resort.