I think Prop 8 will survive, but will be eventually overturned by another amendment. After the massive gay backlash against the Mormon Church, religious institutions will think twice before donating money or advocating against gay marriage.
Churches are institutions that live or die based on public good will, they need converts and regular attendees to sustain them. Having gay activists outside your building calling you Nazis, and attacking you on blogs and newspaper pages, is the last thing a church needs. Mormons especially have a big problem with their public image, and the Prop 8 backlash definitely hurt them.
I think Prop 8 will be challenged by ballot either 2010 or 2012.
I don’t think the backlash hurt mormons at all - if anything, it showed mormons (myself included) what kind of fight we are in. Additionally, the fact that we supported Prop. 8 so strongly and received so much attention for it, if anything, led to greater acceptance of mormons (as people) among different Christian denominations (afterall, we are all in the same fight).
Generally (speaking on my behalf and not that of the LDS Church) >mormons do not care what people think about us, especially if they hold those feelings because they despise our values. We are the descendants of people who left their homes in Europe, and across America for the beliefs that we have. A couple of protests and threats will not convince us to leave those values.
I don’t know what other churches will do, but this mormon, and every other mormon I know has only been fired-up and convinced that we must win this fight.