More than likely, a challenge will be filed and they will try to expedite it. Mitch McConnell is carrying the water on this for now. Anyway, the effective date of the bill isn't until November 6, 2002 so the court may not even hear it by then. That means a decision by May of 2003.
Perhaps if the administration joins in it may happen sooner. I don't know all the legal ramifications but I do know that W cannot just sit on the bill.