The British were not particularly interested in the Americans. Instead, it was their obsession with the French that led them to restrain trade and impress seaman. Their policy of allying with the Indians and expanding Canadian power was, however, a residual result of their distrust of the United States, and it could well have become a major focus of their follow-on strategy after the defeat of Napoleon.
The United States could not tolerate having the British control trade routes in the North Atlantic. Nor could it live with the British maneuvers in North America. Regardless of desires for peace with everyone and the avoidance of war, the United States accordingly declared war on Britain. Although the war resulted in the burning of Washington, the ultimate strategic outcome of the war is generally regarded as satisfactory to the United States. The British stopped threatening the Midwest from Canada, ended impressment (having defeated Napoleon, they didn't need it anyway) and returned to a distrustful but amicable trade relationship with the United States.
This account wouldn't be complete if I didn't mention the Monroe Doctrine, issued in 1823 with the goal of regulating the extent to which European powers could be involved in the Americas. Originally considered a joint U.S.-British document, the United States ultimately decided to announce the principles itself. (It wasn't called the Monroe Doctrine until much later.) Interestingly, the United States was in no position to enforce the doctrine; it could do so only in cooperation with Britain. Yet even so it asserted its unwillingness to allow European powers to intrude in the Western Hemisphere.
A History of Inevitable Alignments
Where Jefferson spoke of entangling alliances, it might be said that no alliances were signed, but alignment was pursued. From the beginning of the American project, entanglement in Europe was inevitable. The republic was born from that entanglement and survived because of the skill and cunning with which the founders managed their entanglement. What is important for today is that economic self-sufficiency was a dream of the founders, albeit one they could never achieve. They had to have trade, and from the beginning, trade brought conflict and war.
In his farewell address, frequently cited as an argument for avoiding foreign adventures, George Washington had a much more complex and sophisticated approach than Jefferson's one-liner did (and Jefferson himself was far more sophisticated than that one-liner). It is worth extracting one section:
"Europe has a set of primary interests which to us have none; or a very remote relation. Hence she must be engaged in frequent controversies, the causes of which are essentially foreign to our concerns. Hence, therefore, it must be unwise in us to implicate ourselves by artificial ties in the ordinary vicissitudes of her politics, or the ordinary combinations and collisions of her friendships or enmities.
Our detached and distant situation invites and enables us to pursue a different course. If we remain one people under an efficient government, the period is not far off when we may defy material injury from external annoyance; when we may take such an attitude as will cause the neutrality we may at any time resolve upon to be scrupulously respected; when belligerent nations, under the impossibility of making acquisitions upon us, will not lightly hazard the giving us provocation; when we may choose peace or war, as our interest, guided by justice, shall counsel.
...Taking care always to keep ourselves by suitable establishments on a respectable defensive posture, we may safely trust to temporary alliances for extraordinary emergencies."
Washington noted that American distance gave it the hope that "the period is not far off when we may defy material injury from external annoyance." For him, this was a goal, not a reality. But he could not make it a reality because the United States was economically entangled with Europe from the start, and its geography, rather than protecting it from entanglement, forced it into trade, which had to be protected against pirates and potentates. As a result, the United States was fighting in the Middle East by the turn of the 19th century.
It is important to distinguish what the founders wished from what they did. Unlike the French Revolutionaries, who took the revolution to its bloody reduction ad absurdum, the Americans had modest expectations for their revolution: They wished for a time when they weren't drawn into conflict. But as we have seen, they were neither surprised nor reticent when conflict proved necessary. It was Jefferson, after all, who led the country to its first Middle Eastern adventure.
For me, the crucial line from Washington is the search for the time "...when belligerent nations, under the impossibility of making acquisitions upon us, will not lightly hazard the giving us provocation; when we may choose peace or war, as our interest, guided by justice, shall counsel."
It's not clear that that time has come or that it will come. What undermined the peace Washington and Jefferson craved was the need for trade. It made the United States, weak as it was, vulnerable to Britain and France and even the Ottomans and forced the United States to engage in the very activity Washington and Jefferson warned against. Indeed, Washington and Jefferson were forced to engage in that activity. The United States is much more powerful today, and its gross domestic product constitutes more than 20 percent of the GDP in the world. The vastness of the American economy causes it to intrude everywhere, and American interests and foreign resentment constantly create threats and challenges.
The desire of the president, the left and the right to limit our engagement is understandable. The founders wanted their prosperity without paying the price of foreign entanglements, but prosperity depended on careful management of foreign relations. Today the vulnerabilities of the United States are much more subtle and complex, but the principle remains the same. You cannot be economically entangled in the world without also being politically and militarily entangled. What you can do is what Washington and Jefferson did: have a clear sense of the national interest and justice and avoid all entanglements but those that are necessary against this measure. Unfortunately, the national interest and justice are not always easily defined, and it is harder still to reach a consensus on what is to be done.
The idea of withdrawing from the world is appealing to any reasonable person. But Washington and Jefferson couldn't do it even though they extolled it. It is unlikely that it can be achieved today. The best we can do is to be ruthless in deciding what entanglements are valuable and what will drain us.