Dempsey would be a good sign at a reasonable price, but we shouldn't overpay for him. He's a bit one dimensional, and I'm not sure of the role he'd play on this team. I don't think he's particularly creative either.
If we sign an American, I think a real shot in the dark (and this probably won't happen, so don't jump down my throat) is Benny Feilhaber who is currently at AGF Aarhus. He's a brilliant passer, extremely creative in the center midfield, only 25 years old, and I think has a decent amount of potential still left. He looked really good in the World Cup as well; his presence changed the Slovenia, Algeria and Ghana matches.