Chasm: That's not quite accurate either. Tax brackets are applied to marginal income, not your entire income. Each segment of your income is charged at the appropriate bracket.
To contrive an example: suppose the tax rate is 10% up to $10,000, 20% for income from $10,001-$20,000, and 30% for $20,001+. Let's say you earn $30,000. You're in the 30% tax bracket, but that does not mean your total tax will be $30,000 * 30% = $9,000. Instead, you pay 10% on your first $10,000 of income ($1,000), 20% on your second $10,000 of income ($2,000), and 30% on the remaining $10,000 ($3,000) for a total tax bill of $6,000.
To take a less contrived (real life) example: that's why everyone above a certain income got $300 back last year. The 15% tax bracket, which happened to be the lowest, was lowered to 10%. That rate applied to the first $12,000 of income, so the total tax on everyone's first $12,000 of income dropped from $1,800 to $1,200. The $300 you got back represented the tax you overpaid for the first half of the year. (For the second half of the year, the amount withheld from your paycheck for taxes dropped about $50/month). Everyone whose adjusted gross income was over $12,000 will pay exactly $1,200 at the 10% rate... no more, no less.
So to sum up: you can make all the charitable deductions you want, but you can't "fall into a lower tax bracket for the remaining income." That remaining income is already being taxed at the lowest available rate. The good news is that deductions reduce the amount of income you have that's taxed at the highest bracket you're in.
Repetition of disclaimer: I'm not a tax attorney. Consult your accountant before making any major financial decisions for tax purposes.