It depends. There are two different questions here but I hope to answer both of them.
NJ taxable income could be higher than federal income. This is because there are some items that are taxable in NJ that are not taxable at the federal level (one example is a retirement contribution that is not a 401K). Here is a website that explains this in a little more detail: http://www.state.nj.us/treasury/taxation/njit5.shtml
While the amount of taxable income may be higher for NJ over Federal taxable income, it should only be moderately higher. If you see that what is taxable in NJ is substantially higher, then there is a question that asks about double-taxed income (I believe it is the same screen you refer to in your question). For this question you would enter the NY income as the double-taxed income. This amount should bring your NJ taxable income (and tax) to the correct amount.
Your second question is in regards to the credit given by NJ for taxes paid to another state. In this case, NJ gives a credit for the tax you must pay to NY on the income earned in NY, but only up to the point that NJ taxes the same income. Thus, if NY has a higher tax rate on the income than NJ, you don't pay any NJ tax on that income. (However, since NJ does include as taxable income amounts not taxable on the Federal or NY returns, you may still have an amount due to NJ on the income that is only taxed in NJ and not NY).
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