A fair number of political voices in the US, including former Republican candidate John McCain and several bloggers on the right of the spectrum, have been critical of President Obama's caution on Iran and have been urging a more open support for the protesters. I can't think of a more certain way to undercut the Mousavi supporters.
Back when I was discussing Eric Davis' "Ten Sins" in Middle East analysis, in the discussion of "Presentism," I noted that Iranians tend to be more historically aware of the US-backed Operation Ajax in 1953, when the US destabilized Mossadegh, than Americans are. Believe me, Iranians remember that, and many of the liberal protesters are the intellectual heirs of Mossadegh's followers. Believe me, too, that US support of the Shah has been drilled into everyone's consciousness through 30 years of revolutionary rhetoric.
Any open support the US offers, other than the cautious sort of comments made so far by Obama, could be used by the regime against the protesters. Being able to paint Mousavi and his backers as American puppets — and Ahmadinejad is trying hard to do that — would guarantee the outcome. We're the "Great Satan," remember? And Mousavi was Foreign Minister and Prime Minister in the days of Imam Khomeini himself: his approach has been to call for returning to the principles of the revolution, not to the policies of the monarchy.
I'm not talking here about private citizens: Bloggers who change their website color to green in empathy, for example, or the Twitter posters who last night were urging others to change their location and time zone to make it appear they were in Iran, in order to confuse the security forces trying to track down tweeting Iranians. What I'm talking about is any open governmental support such as McCain and others seem to be calling for. That would be precisely the wrong thing to do.