The following comes from Dan Graziano at FanHouse:
One of the sources said that Washington was the only team still in the mix to trade for Bradford, who has told the Rams he won't sign a contract until after he is drafted. The Seattle Seahawks and Cleveland Browns -- two teams that had interest in Bradford -- are no longer making the effort to try to trade up and get him. [...] But as of Wednesday night, even with McNabb on board, the offensive line a lingering concern and no picks in the second or third rounds, the Redskins were apparently still working on a way to come away with the draft's biggest QB prize.
It might seem a little strange, trading to get a young quarterback after they just made the effort to bring in Donovan McNabb(notes), but if it were to happen, I'd love the move for the Washington Redskins.
If you feel like Bradford can be a franchise quarterback for the next 10 years, then it's worth moving mountains to get him. I love Donovan McNabb, and I believe he is a franchise quarterback, but unless he develops Richard Alpert syndrome, it certainly won't be for the next 10 years.
Pro Football Talk says that if anyone's going to move into the Rams' spot, it's more likely to be the Cleveland Browns. They're hurting at the quarterback position, far worse than the Redskins, and they've got more draft picks to play with in exchange.
I still think the most likely thing is that the Rams stay put, take Bradford, and live happily ever after with him.