Actually, in an 82 game season, they play 24 in their division (~29%). They will be playing 18 of the 48 in division this year (37.5%). Not really a huge jump.
It's the 48 games overall in the 3 months that will be more taxing than the physical nature of the division teams. What will be interesting to see is if physical play, minus rival games, is at the normal pace we're used to seeing up until closer to playoff time just because players will be trying to save energy and not get hurt with playing so many games in so little time.