It is simply impossible to go from Nagoya to Sapporo in one day. From Tokyo you could do it by leaving first thing in the morning, then arriving at Sapporo very late at night. It simply is not practical.
In this case, the only smart choice is to fly. Fortunately, there are cheap options available for this.
There are low cost carriers like Jet Star that can fly you up, even for as little as 6000 yen one way, depending on when you fly. See:
http://www.jetstar.com/jp/en/home
Another option are some air passes, both are available from ANA and JAL. Prices vary depending on which international carrier you are taking to Japan, and there are some blackout dates for most fares (except the Experience Japan fare).
See:
http://www.jal.co.jp/yokosojapan/
Your JR Pass might still save you money, depending on your whole itinerary. Otherwise, it can be refunded. The only other choice would be to break up your rail trip from Nagoya to Sapporo into 2 days, stopping somewhere along the way. It still means a lot of time sitting on a train. Sorry about that.