In warfare and in political warfare, underestimating your opponent amounts to a terrible, often fatal mistake. That's why conservatives who deny or ignore the president's obvious intelligence imperil their own cause and prevent the emergence of an effective anti-Obama strategy. For Barack Obama, his brain power makes him dangerous but also creates a special vulnerability that his critics should exploit.
On the most obvious level, it makes no sense to insist (as many of my radio callers and internet correspondents do) that a guy with degrees from Columbia and Harvard Law (magna cum laude), and with a successful twelve-year stint as a professor of Constitutional law at the University of Chicago, amounts to some sort of dunce who didn't deserve his academic success. The Democrats made similarly silly assumptions about George W. Bush, claiming that his BA from Yale and his MBA from Harvard Business School stemmed only from family connections rather than personal ability or hard work. In Obama's case, some right wingers argue that he got his Ivy League credentials through affirmative action and race preferences. It's true that favored minority groups may receive special encouragement at elite universities, as do alumni children with multi-generational connections to the institutions in question. But unless an applicant counts as at least reasonably bright in his own right, neither ethnic identity nor parental pull can assure admission, let alone graduation. Even among targeted minority groups or alumni children, those who succeed at top flight, competitive universities constitute a distinct minority.
Moreover, with President Obama three other factors argue powerfully that he's a genuinely intelligent individual no matter how misguided his political priorities and outlook.