Indeed, in retrospect what’s shocking about the miscalculation on the war vote is less its simplistic nature—the war authorizing resolution was high-profile and popular, so Shrum advised his clients to vote for it. But neither Kerry nor Edwards was in a tough 2002 reelection battle. It didn’t matter whether or not the resolution was popular. A politician who took a stand against it would have two years to wait for events to vindicate his view. As, indeed, the skepticism about the war that Shrum attributes to Kerry and Edwards was vindicated by election day 2004. Which might have done them some good had they actually made the right call. The view that good policy is good politics sounds sappy and naive, but on this kind of issue it’s true—the first thing you need to ask yourself when trying to decide whether or not backing some invasion will be politically savvy is what you think will happen if the invasion actually takes place.
The only flaw in this line of reasoning is that it's possible to think that a war will prove both misguided and enduringly popular. Maybe, as Matt suggests, Kerry and Edwards thought that Iraq would be a disastrous mess by 2004, in which case he's right: Their votes made no sense as policy or politics. But maybe they thought that the Iraq War was a bad idea because the doctrine of pre-emption set a dangerous precedent, or because they thought that invading Iraq was a distraction from the hunt for Bin Laden, or because they feared long-term blowback from further U.S. adventures in the Middle East - all of which would have been reasonable reasons to oppose the war, but none of which would have given them confidence that they would be vindicated in the court of public opinion any time soon. Opponents of the First Gulf War, for instance, would argue that the events of 9/11 vindicated their concerns - because the Gulf War created a permanent U.S. military presence in Saudi Arabia, providing grist for anti-Americanism across the Islamic world - but there hasn't been a massive post-9/11 backlash against George H.W. Bush or Brent Scowcroft, to say the least. Or to take a more remote example, I'm inclined to think that our intervention in the First World War was a strategic mistake and that both the Spanish-American War and the Mexican War violated just-war principles - but had I been an anti-war politician in 1914 or 1899 or 1846 I would have suffered politically for taking these stances, regardless of whether I was right on the merits.
Nobody can know for sure, obviously - and Edwards' own explanation of his vote for war, as Matt points out, is further muddling the issue - but I suspect something like this thought process was at work in the Shrumian assumption that opposing the invasion of Iraq made for bad politics.