Based on what you write, it's hard to tell whether you know this or not, but there is not a one-to-one tradeoff of charity money and tax money. Charitable contributions give a tax deduction, not a tax credit.

So, for a hypothetical person with a $50,000 income and a tax bill of 20%/$10,000:

If she gives $10,000 in tax-deductible charitable contributions, her tax bill only drops to 20% of $40,000, or $8,000.

The only way for her to get to $0 tax due is to give all of her income to charity.

The above isn't exactly true, as the math is complicated by the other deductions she will have (essentially, giving to charity for most people is not a tax deduction at all unless they have enough deductions so that the total adds to more than the standard deduction, which it won't for most people), as well as progressiveness in the tax code.