Bringing a group with a marginal commitment to democracy into democratic politics has its risks but also a benefit - the group starts accepting democratic norms at some level, and eventually learns the art of compromise.
So now we see what happens when the same groups feel taken for fools:
But at the same time, Sheik Abu Sidra said, Mr. Morsi’s overthrow had made it far more difficult for him to persuade Benghazi’s Islamist militias to put down their weapons and trust in democracy.
“Do you think I can sell that to the people anymore?” he asked. “I have been saying all along, ‘If you want to build Shariah law, come to elections.’ Now they will just say, ‘Look at Egypt,’ and you don’t need to say anything else.”
From Benghazi to Abu Dhabi, Islamists are drawing lessons from Mr. Morsi’s ouster that could shape political Islam for a generation. For some, it demonstrated the futility of democracy in a world dominated by Western powers and their client states. But others, acknowledging that the takeover accompanied a broad popular backlash, also faulted the leaders of the Muslim Brotherhood for reaching too fast for so many levers of power....
“The message will resonate throughout the Muslim world loud and clear: democracy is not for Muslims,” Essam el-Haddad, Mr. Morsi’s foreign policy adviser, warned on his official Web site shortly before the military detained him and cut off all his communication. The overthrow of an elected Islamist government in Egypt, the symbolic heart of the Arab world, Mr. Haddad wrote, would fuel more violent terrorism than the Western wars in Iraq and Afghanistan.
And he took aim at Western critics of the Islamists. “The silence of all of those voices with an impending military coup is hypocritical,” Mr. Haddad wrote, “and that hypocrisy will not be lost on a large swath of Egyptians, Arabs and Muslims...."
In the United Arab Emirates...Islamists said the crackdowns were driving a deeper wedge into their movement.
“The practices that we see today will split the Islamists in half,” said Saeed Nasar Alteneji, a former head of the Emirates group, the Islah association. “There are those who always call for centrism and moderation and peaceful political participation,” he said. “The other group condemns democracy and sees today that the West and others will never accept the ballot box if it brings Islamists to power.”
“And they have lots of evidence of this,” he said, now citing Egypt as well as Algeria.
Of course there's always another hand, and just as Allende rashly governed as if he had won a broad victory instead of 36% of the vote in a not-very-democratic democracy, Morsi went and alienated potential partners in a divided country. In all the discussion I've seen, people acknowledge that democracy isn't just about elections but haven't expressly referred to the right to revolution, something that's been part of the traditional democratic theory for centuries. You could argue that's what happened, although a military coup in support of popular protests doesn't quite fit the archetype.
Regardless though of whether the protesters had the right to do what they and the military did, is whether Egypt and the Arab world is better off for it. I don't think Morsi was completely beyond compromising. A Muslim Brotherhood government maintained a peace treaty with Israel - I'd like to see the analyst, especially in the pro-Likud faction in the US, who predicted that. If the popular protests were truly popular, then barring real movement from Morsi, we would've seen the results in the next elections, but his opponents weren't willing to wait.
Morsi wasn't smart enough to offer snap elections. Had he been smart enough, maybe he also wouldn't have made the other mistakes that brought him to this point. One advantage a long-standing democracy has over a new one is that people like him have usually gone through a lower office election or two and make their career-ending mistakes earlier on. The trick is to get to a stable democracy though, and overthrowing a government every time its leader is stupid will not get you there. Hopefully they'll do better the next time.
As for what the US should do, I'm not sure. If Egypt gets elections soon, then we might as well just find a way to contort around the prohibition of military aid after a coup. Otherwise, start cutting the military off.