Final answer:
Congress disagreed on going to war with Britain due to the differing interests between 'war hawks' and Federalists. The 'war hawks' felt British actions were insults to American honor, while Federalists feared the disruption of maritime trade. The Continental Congress prepared for war anticipating the possibility of military action being necessary.
Step-by-step explanation:
Congress disagreed about going to war with Britain for several reasons. The seizure of American ships and sailors, and the British support for Native American resistance were significant factors that fueled the desire for war, led by 'war hawks' such as Henry Clay and John C. Calhoun. They felt that British actions were direct insults to the American honor. On the other hand, there was strong opposition from the Federalists, particularly in the Northeast, who depended on maritime trade and knew that war would disrupt this vital industry. Despite the division, Congress authorized the declaration of war against Britain in a narrow vote in June 1812.
The question about whether anything could have been done by Jefferson or Madison to resolve the conflict and avoid the War of 1812 is complex. Both administrations sought peaceful means to address the issues, such as Jefferson's embargo, though ultimately, these measures were insufficient in changing British policies, which were heavily influenced by the Napoleonic Wars in Europe. Regarding the burning of Washington D.C., while it can be seen as a military strategy in the context of the war, it is typically viewed as unnecessary and vengeful, as the action targeted non-military infrastructure.
The Continental Congress created an army and started preparing for war prior to receiving a response to the Olive Branch Petition because there was a prevailing sense of urgency and the belief that military preparations were necessary. They sensed that peaceful reconciliation might not be successful given Britain's previous reactions to colonial grievances. The events at Lexington and Concord, which resulted in the first American casualties, occurred before the Second Continental Congress convened, underscoring the need for an organized military defense.