The Isles actually spent three days (Oct 10-12) all alone in first place, after a 2-1 win over the Rangers on October 10th. They played on October 11th, but lost 8-1 to Toronto.
The Isles have not been in first place after Christmas in any season since the 1995 lockout campaign. They opened that season 2-0-1 and had the divisional lead by themselves as late as January 28 and in a tie on January 29.
To get there on Thursday, it would probably be helpful to score more than one goal. The Devils have held the Isles to exactly one goal in five straight games (although the Isles won the first game, 1-0).