Actually, as a resident of Delaware, you would be taxed on your entire W-2 income derived from all States. Fortunately, Delaware State's Individual Income Taxpayers would be given a tax credit that would be equal to the actual state income tax liability payable to another State Jurisdication (as a result of income sourced to that State, other than Delaware).
Thus, in your case, your income that is sourced from New Jersey State would be subject to NJ State Income Tax. Now, when you file a Delaware Personal Income Tax Return, your entire 2010 NJ Income would be subject to Delaware Income Tax. But, the amount of your 2010 NJ Tax liability would result in a tax credit on your 2010 Delaware Personal Income Tax Return, that would lower your Delaware Income Tax Liability.
Thus, it would mean that you would not be paying double taxation on your NJ Income in Delaware State.