It's possible, because the tax code is complex, but married-filing-jointly has a lower tax rate.

For example, let's assume you both have 40k taxable income:

Single, taxable income 40k: tax is $5,935

Married, taxable (combined) income 80k: tax is $11,864

Double the tax on "single", because you would file two returns, and you get $11,870. So you actually saved $6!

Taken directly from the tax table: http://www.irs.gov/pub/irs-pdf/i1040tt.pdf