You don't calculate the taxable portion. You calculate the amount that is from U.S. Government securities. It is simply the total ordinary dividends from 1099-DIV box 1a multiplied by the percentage that is from U.S. Government securities, as stated by the fund company.
In the federal income section of TurboTax, after you enter the 1099-DIV, the next screen says "Tell us if any of these uncommon situations apply." Check the box that says "A portion of these dividends is U.S. Government interest." One or two screens later there is a box to enter the U.S. Government interest amount that you calculated. The amount flows to the New Jersey tax return, and TurboTax will make the adjustment on the New Jersey return.