Not Dems, MM, Political parties. They don't have the collective control they need over the presidency. Once the president is there, they can't influence him. In Congress they can keep our representatives on a little string, making sure nothing they want to do gets done, and that they won't be re-elected. Presidents have too much independence, and if parties want to reach out further into international politics they have to subvert the office.
So lets not divert this in partisan terms. Specter is as big a tool as Nelson, and if he doesn't go it will be because of the press this gets. In the end the effort won't change, even if it isn't as overt.