Quick answer: I don't know, but it's less likely than it might initially appear.
Earlier this month several sources, including Wired, reported that over 30 large companies, including Google and Adobe, had been victims of a sophisticated hack, which Microsoft admits was made possible by a weakness in Internet Explorer 6. Microsoft also admits that it learned of the flaw in September, and that it was holding back a patch so that it could be released in a cumulative update that was due out next month. Given the above, and the notoriously litigious nature of the American public, it would seem that Microsoft is almost guaranteed to be hit by a lawsuit seeking damages based on the failure to release the patch earlier. Certainly, when I read that Microsoft had learned about the flaw and withheld the patch, my first thought was that this was something that would keep their lawyers busy in court for months (if not years) to come.
However, the more I think about the situation, the less I think Microsoft is guaranteed to go to court. If this had happened 3-4 years ago, I'd expect Microsoft would already have been hit by a class action lawsuit filed on behalf of consumers who used IE6. However, since that time, courts have been pretty uniformly unreceptive to claims that consumers are damaged by increased risks caused by unauthorized access to data by third parties (e.g., here). A consumer wanting to sue Microsoft for vulnerabilities in IE6 would be even less likely to succeed, since (unlike the unsuccessful plaintiffs in the security breach cases) the hypothetical consumer suing Microsoft wouldn't even be able to show that an unauthorized third party had accessed their system, only that they were at an increased risk of such access due to using IE6. Looking at that history, the chances of a consumer class action against Microsoft seem pretty slim.*
So, consumers aren't likely to sue Microsoft, what about the businesses who were victimized because of the flaw? While they'd have an easier time proving damages (after all, it is known that they were hacked, and at least some of what the hackers did), there are also forces which could prevent them from going to court. For one thing, most businesses try and work things out before involving the judiciary. In this case, I assume that Google, Adobe, et al have contacted Microsoft about helping them clean up the damage. Microsoft has a significant interested in trying to make sure those out of court efforts are successful, since a drawn out court battle could only hurt Microsoft's brand in the already competitive browser market. Similarly, the companies that have been hacked would probably like to avoid going to court as well, since any lawsuit would invariably have the effect of calling their own security into question, even if they could convince the public that the reason their systems weren't secure is because they were using unsafe products, rather than that their own internal practices were deficient.
Of course, strong incentives to avoid a court battle don't necessarily mean there won't be one. If the damage caused by the hackers is too expensive, Microsoft might be willing to fight not to pay it, and the injured company might be willing to fight to get paid. At this point it's impossible to say how likely that is to play out. However, I think, given the incentives on all sides to avoid it, the likelihood of a lawsuit against Microsoft on this is much lower than it would initially appear.
*Obviously, the chances aren't zero. If there was going to be a suit against Microsoft, I would expect it in a state which has allowed suits for increased risk of health problems as a result of a chemical spill. The analogy isn't perfect, but it does make it somewhat easier to prove damages.