With regards to Original Screenplay, not very good. The last time the winner for the National Board of Review award was even nominated for the Oscar for Original Screenplay was five years ago with The Coen Brothers' A Serious Man. And only once did the winner of the NBR award also win the Oscar, Diablo Cody's Juno, which actually tied for the NBR award.
While it would be awesome if The Lego Movie somehow pulls off an upset and gets nominated for Original Screenplay at the Oscars (and I very much believe that the film is worthy of a nomination in that category, though probably not a win), I was thinking more along the lines of, "How likely is it that Academy voters will take note and pay more attention to the film in regards to the Animation category"?
They really don't have to bother, the Oscars have been cribbing the NBOR for half their nominations ever since they changed the rules in '03 and now don't have any time to think of their own.
What was the rule change that happened in '03?