From the article: "The top 1 percent on average already pay roughly a third of their incomes to the federal government, according to a Treasury Department analysis that takes into account the entire menu of taxes — including income tax, payroll taxes that fund Medicare and Social Security, estate and gift taxes, excise and custom duties as well as investors’ share of corporate taxes."
And I found that fraction credible since it's been generally true after the 1986 tax reform (the following Clinton and Bush II tax changes didn't do all that much, especially compared to the Reagan changes).