As Chatterbox has noted repeatedly, the Constitution Party is keen to make Moore its standard-bearer. If Moore runs for president, as he's suggested he might do, Moore has the potential to siphon so many Christian right votes from President George W. Bush as to throw the general election to the presumptive Democratic nominee, John Kerry. Moore, in other words, has the potential to become the Ralph Nader of the right.From what I understand, the Constitution Party already has a presidential candidate, Michael Peroutka. On the other hand, the number of votes Judge Moore would be able to garner on a national level (particularly from disaffected conservatives) would exponentially greater than Peroutka, and as Slate points out, he would have the potential to make a crucial difference in the general election.
From my standpoint (as someone who knows next to nothing about the Constitution Party, but more than a little about Judge Moore), my own guess is that the Constitution Party would be willing to replace Peroutka with Moore if Moore were willing, but that Moore will decline the opportunity.