I am not an accountant, either, but...
Charitable contributions ARE deductible from your income when computing your taxes. This assumes that you are itemizing your deductions, and that the recipient has the proper charitable status with the IRS. There is also something called the "alternative minimum tax" that may apply to some folks and may prevent them from reducing their taxes to zero. But other than that, sure, if you give away enough money, you can reduce your taxes to zero.
Note that contributions are deductible from your income when computing your taxes, NOT from the tax amount as the first post here implies. Perhaps this is what Sig meant. Also note that we are talking about the amount of tax for the year, not the amount of tax withheld.