Egypt today is a zero-sum game. We'd have preferred there be a democratic alternative. Unfortunately, there is none. The choice is binary: the country will be ruled by the Muslim Brotherhood or by the military.
Perhaps the military should have waited three years for the intensely unpopular Mohammed Morsi to be voted out of office. But Gen. Abdel Fatah al-Sissi seems to have calculated that by then there would be no elections — as in Gaza, where the Palestinian wing of the Brotherhood, Hamas, elected in 2006, established a one-man-one-vote-one-time dictatorship.
What's the U.S. to do? Any response demands two considerations: (a) moral, i.e., which outcome offers the better future for Egypt, and (b) strategic, i.e., which outcome offers the better future for U.S. interests and those of the free world.
As for Egypt's future, the Brotherhood offered nothing but incompetent, intolerant, increasingly dictatorial rule. In one year, Morsi managed to squander 85 years of Brotherhood prestige garnered in opposition — a place from which one can promise the moon — by persecuting journalists and activists, granting himself the unchallenged power to rule by decree, enshrining a sectarian Islamist constitution and systematically trying to seize the instruments of state power. As if that wasn't enough, after its overthrow the Brotherhood showed itself to be the party that, when angry, burns churches.
The military, brutal and bloody, is not a very appealing alternative. But it does matter what the Egyptian people think. The anti-Morsi demonstrations were the largest in recorded Egyptian history. Revolted by Morsi's betrayal of a revolution intended as a new opening for individual dignity and democracy, the protesters explicitly demanded Morsi's overthrow. And the vast majority seem to welcome the military repression aimed at abolishing the Islamist threat. It's their only hope, however problematic, for an eventual democratic transition.