You can read about them...
http://en.wikipedia.org/wiki/MoveOn
And check them out if you haven't already...
http://www.moveon.org/
I think it's a pretty big deal, they've had some success backing political candidates.
The idea that Obama is moving towards the left is a quote straight out of the Conservative 'Think Tank', the race is about the center, the all important biconseptual vote, and who they will vote for in November. As long as THEY convince the public (through the media) that Obama is moving left, the floating vote will shift towards McCain. At least I'm sure that's what they're "Thinking".
Don't let them frame THEM frame the debate.
And on a side note, what's wrong with the word "Left" anyway?