How about if the USA had overextended itself closer to home, perhaps in the Caribbean? For instance, if the United States' Invasion of Grenada in 1983 had been publicly opposed by Margaret Thatcher as opposed to merely privately opposed by her, and had been met with a concerted guerrilla effort from the Cubans and Grenadians, forcing a lengthy occupation to try and dislodge them and resulting in far more civilian casualties?
This also leads Reagan to stand his ground on the ongoing Guatemalan Civil War, and instead of merely increasing military assistance and cooperation with the Guatemalan government, he also authorises an increase in the USA's military presence in Guatemala, deploying for the first time ground combat units to try and bring it to an end, and essentially turning the Guatemalan Civil War into another 'Resistance War Against America', just like the Vietnam War. The resulting backlash greatly increases civil discontent among the American populace, with the overwhelming majority (especially among the Latino community) believing the war to be fundamentally wrong and immoral.
And it also results in a far greater upsurge of support for the Workers' Socialist Movement in Puerto Rico, and the emergence of an armed insurrection in Puerto Rico by advocates of socialist and independent Puerto Rico, which in turn is brutally supressed by the American authorities. This is further exacerbated by the annexation of Grenada as a US territory by the USA, and after the collapse of the Soviet Union, the 1996 shootdown of Brothers to the Rescue aircraft triggers a declaration of war against Cuba by the United States, and another invasion of Cuba, which becomes the final straw for many of the rest of the world's nations, and for much of its own populace.