My husband lives in NJ and worked in NYC up until Nov 2008. When I went to file our taxes through Turbo Tax it says we owe over $2000 in NJ state Tax when I entered his NY and NJ W-2's. He only made around $55,000 in total between the 2 jobs, they are with the same company he just transferred to a location here in NJ. He paid NY taxes and paid NJ taxes for the 2 months he worked here in NJ... why would we owe so much money to NJ.

You will report your NYC income on tax return for both the states.
On NJ state return, you will also claim credit for taxes paid to NY. Read: Your U.S. Tax Return: Working or Living in Two or More states

When you properly claim a credit on your NJ return for the NY state and NY City income taxs paid, the NJ amount owed should go to ZERO, because the NY state and NY City tax rates far exceed the NJ tax rates.