Your tax liability is the total amount of taxes you owe for the year. It is Line 24 on your tax return. Some credits are refundable and some are non-refundable. You are describing a non-refundable credit, although I am not sure which credit you are referring to. Non-refundable credits can only lower your tax liability to zero; they can't generate a refund. With non-refundable credits, you have to owe taxes to get any benefit. If your tax bill is zero, a non-refundable tax credit won't change your tax return.
Some credits do carry forward so you can use them in later years, while other credits are only available in the current year. Which tax credit are you claiming? More information on tax credits can be found here.
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