The exact wording of the law actually stipulates a $6,000 tax deduction for individuals aged 65 and older, likely raising the number of seniors who won't pay taxes on Social Security to 88 percent. Currently, 64 percent of seniors already don't pay taxes on Social Security benefits.

The exact dollar amount you'll save depends on several factors, including your annual income and tax filing status. A Council of Economic Advisors report estimates that the average senior who qualifies for the new tax deduction will see an increase of $670 in after-tax income. But it's possible that you may save slightly more or less than this.