Yep. It's a major strategic and symbolic target. You'd better believe that if that got taken out, people would remember it down the years. Incidentally, if the nutters are making enemies lists, which I find not at all far-fetched, nasty, vindictive little turds that they are, you have to figure Dubya and his family (Laura and the girls at the very minimum) are high up.
The one flaw with "the White House" is that it wouldn't shock the narrator of the story that much, or be horrific next to the stuff he's already heard. But yeah, it's got to be very high on their lists.