> I thought in the US system, swinging votes don't really matter. Those fence sitters aren't confident or interested enough to vote anyway. I thought the only thing that mattered was preaching to the choir & getting them to vote at all.

Not at all. While you don't have a chance if your base doesn't come out, they almost always do. As a result, swing votes typically decide US elections.

There are, however, two kinds of swing votes. One always votes, but switches. The other shows up occasionally.