The Iowa Caucuses might end up being held on January 3, but we won't know the official date until next week at the earliest.
Frontolading HQ reports that both Iowa and New Hampshire potentially want the January 3 spot, and a dangerous game of chicken that could end up with New Hampshire moving their primary to December 6 in order to comply with their state law and keep the attention heir state gets from having "first in the nation" status.
This boils down to a battle of the wills or a battle of the systems of moving primaries and/or caucuses. Iowa Republicans have the freedom that any state party has. They can move their contest around without checks. New Hampshire has that, too because the state handed that power over to one person -- the secretary of state -- in 1975. What New Hampshire also has is state law that requires seven days between it and the next contest. Now, we can argue about the latitude granted Secretary Gardner in that law -- that "similar contest" portion provides some leeway, albeit limited -- but the simple truth of the matter is that Gardner has already deemed the Nevada caucuses on January 14 to be "similar". He's not likely to change that opinion.
Regardless, Gardner holds the trump card. He is seemingly willing to take New Hampshire into December if need be to protect the law. Whether that's true or not, we may never know, but he is seemingly willing to play it. And Iowa Republicans are not willing to slip into December.
I'm slightly more inclined to say advantage New Hampshire, but Iowa Republicans could ultimately prove to be a lot like the Nevada Republicans were earlier this week. Frustrated by Gardner's insistence on following the law, the Nevada Republican Party ultimately shrugged its shoulders and said, "Screw it. We'll set a date. To hell with New Hampshire. Let them do what they will." That didn't call Gardner's bluff. That responsibility now rests with the Iowa Republican Party.