First, it's important to remember that the Iranian election isn't about us. The vast majority of Iranian voters were angry about Iran's domestic economy. Opposition to Amahdinejad came primarily from the ongoing poverty in Iran in the face of vast oil wealth, not an opposition to the Islamic theocracy. One reason that the blatant election fraud seems so strange is that Moussavi is also supported by, and a strong supporter of, the Islamic council that is the true power in Iran. It's really unclear to me why the Ayatollah (and the supreme council) chose to rig the election, since the real power (and control of the Republican Guard) would remain unchanged, regardless of who won a legitimate election. By engaging in such blatant disregard of the voters will, they've actually weakened their own position. The Islamic Republic was under no threat from Moussavi. Now they are under threat from the massive public outcry.
Second, there is the history of mass protest in Iran from 1979. Each death leads to an additional demonstration of mourning. The 1979 revolution only came about after almost a year of daily demonstrations. So crackdowns will continue to bring more people out into the streets, and further weaken the government control as family loyalties (the strongest bond in Iranian society) tax the guards loyalty to the government. The Shah lost when his guards defected to join their brothers and sisters in the Green Bands (side note to media pundits: the Green Bands were the Islamic militia in 1979; wearing green bands still symbolize support for Islamic law, not some sort of western ideal of "freedom fighters"). This may take a while to play out.
Thirdly, Obama seems to be doing the right thing, by trying to remain uninvolved. He's walking a tightrope, but faced with the history of American meddling in Iran, support for the protesters is bound to backfire. The Iranian government is already portraying the demonstrations as the result of foreign provocation. Regardless of America's preference, Obama will need to deal with the eventual victor, and any American endorsement will only poison future relations.
While I said earlier that this isn't "about us", it's certainly clear that America would prefer to see Amahdinejad out of power. Amahdinejad's bombastic anti-American and anti-Israel rhetoric has made it almost impossible to conduct any realistic dialog with him. He's created an adversarial relationship, and shrub and the neocons were perfectly willing to engage as adversaries. It's almost impossible to negotiate when both parties start by calling the other "evil". Moussavi is anti-American and anti-Israeli, but he's much calmer in his rhetoric than Amahdinejad, so there's a chance to open talks with a 'clean slate' (in reality, a less tainted slate), or at least without the baggage of recent years. I doubt that it will be a 'warm friendly' relationship, but it would allow us to pull back from the brink of war.
Those Mousavi supporters are using the slogans of the Islamic Revolution and it's my understanding that they are mostly simply seeking a return to the status quo ante, when their votes meant something in the half-rigged Islamic Republic's system. They're not looking to depose the mullahs and they're not looking to break the system that's persisted since 1979 - they just want it to work as advertised. Nowhere is this clearer than in their choice of leaders: Mousavi, Rafsanjani, Khatami, Montazeri. All members in good standing of the Iranian politico-clerical elite and all standing to gain nothing from a break-up of the existing system. As Trita Parsi writes:
What's often forgotten amid the genuinely awe-inspiring spectacle of hundreds of thousands of long-suppressed people risking their lives on the streets to demand change is the fact that the political contest playing out in the election is, in fact, among rival factions of the same regime. Ahmadinejad represents a conservative element, backed by the Supreme Leader, that believes the established political class has hijacked the revolution and enriched themselves and is fearful that the faction's more pragmatic inclination toward engagement with the West could lead to a normalization of relations that will "pollute" Iran's culture and weaken the regime. Mousavi is not really a reformer so much as a pragmatic, moderate conservative who has campaigned with the backing of the reform movement because it recognizes that he has a better chance of unseating Ahmadinejad than one of their own would have.