Dodd is correct that his fellow candidates backed an amendment he co-sponsored. And it's likely that they felt some pressure from liberal Democrats -- including Dodd -- who strongly favor withdrawal.
But Dodd exaggerates his role. He is just one of nine co-sponsors of the amendment widely called the Feingold-Reid amendment, usually without Dodd's name attached. And both Clinton and Obama have advocated other troop withdrawl proposals before endorsing this one. There's no evidence that Dodd had any influence on Obama and Clinton.