I've run the numbers on the family of four (2 adults, 2 children). The family income can be $47,599.49 for tax year 2014 and no income taxes will be paid based solely on the standard deduction, personal exemptions x 4, and the child tax credit x 2 or, in other words, the makeup of the family. If there are any other credits/deductions, the amount goes up. If the amount hits $47,600, the tax is then $6.
I didn't count the mortgage interest deduction as that is only allowed if itemizing. I used the standard deduction. Again, if the itemized is greater than $12,400 (standard), the income level before paying taxes goes up.
While that's not wealthy, it's 200% of the poverty level for that size family.