The economy takes a double-dip recession in late 2010, and unemployment is still above 9% or perhaps rises above 10% again. The Democratic party loses more seats than expected, hanging onto a slim majority in Congress. More importantly, several existing and new Republican seats in the House go to ultra-right "Teabagger" sympathizers.
The economy worsens between 2010 and 2012. Civil unrest grows, especially in the inner-cities (read "Black"*) and among industrial labor. A charismatic and strong leader of the ultra-right Teabagger faction gains national prominence. His or her platform rests squarely on oppression, expulsion and barely-concealed eliminationism of immigrants, socialists, Muslims and atheists to purify America of the corrupt elements that are holding us back. (Add a healthy dose of racism and misogyny on the side.) He or she also promises to put America back to work (by intensifying and expanding the wars in the Middle East). The Teabaggers act violently, often against other protesters, but also against a few select (relatively) moderate or especially recalcitrant Republicans.
*i.e. I expect black people to get screwed by the economy extra hard.
President Obama is severely weakened by the mid-term elections. He tries to become more confrontational and combative, but it's too little, too late. Additionally, in a series of PR blunders, the existing Republican party leadership alienates the Christian right. The Republican party, with severe internal divisions, nominates a dark horse candidate. Neither Obama nor the Republican nominee have a strong popular showing in 2012, with the incumbent Obama having a slight plurality. The Teabaggers run a third-party candidate who secures about 20% of the popular vote.
One of three things might then happen: The Teabagger candidate might actually win a state, giving him or her representation in the Electoral College. It's possible too that state-level Teabaggers might get proportional representation passed in one or more red states, giving the Teabagger candidate at least one electoral vote. It's also possible to directly suborn one or more of the Electors: at least some are not legally compelled to vote for the candidate they're pledged to. If the election is close, just a few votes in the Electoral College would be enough to deny both the Democratic and Republican candidates a majority.
The election is thrown to the House of Representatives, who consider the top three candidates from the Electoral College vote: a Republican, a Democrat and a Teabagger. This is the moment for the big putsch.
The 12th Amendment structures the House vote for president weirdly. The congressional delegation as a whole from each state has one vote. Because there are fewer, more populous Democratic states, it's virtually impossible for Obama to win... unless the Teabaggers, who have enough representation in enough states, throw the vote.
They make a bold bluff, and threaten to vote for Obama unless the Republican states vote for the Teabagger. A near-riot crowd of Teabagger supporters surrounds the Capitol, and there's demonstrations and rioting around the country. There are also hints of violent retribution for "recalcitrant" Republicans. The Republicans turn to the conservative Democrats, to no avail: they hope that the Teabaggers aren't bluffing. With partisan animosity and what little party discipline remains to the Democrats, it's not enough. The mainstream Republicans must choose: the Teabaggers or Obama.
The mainstream Republicans blink. Of course they blink. They respect power. A few phone calls, perhaps from
Why not? Hitler's machinations were no more plausible.