I'm quite annoted at the substance of the original post, or the lack thereof. Let's fix that.
First off is a direct link to the paper: http://www.taxpolicycenter.org/sites/default/files/publication/144971/a_preliminary_analysis_of_the_unified_framework_0.pdf 
All emphases going forward are added by me, to denote a direct quote. Bolding is for emphasis.
In 2018, the average tax bill for all income groups would decline. Taxpayers in the bottom 95 percent of the income distribution would see average after-tax incomes increase between 0.5 and 1.2 percent. Taxpayers in the top 1 percent (incomes above $730,000), would receive about 50 percent of the total tax benefit; their after-tax income would increase an average of 8.5 percent. Between 2018 and 2027, the average tax cut as a share of after-tax income would fall for all income groups other than the top 1 percent. In 2027, taxpayers between the 80th and 95th percentiles of income (between about $150,000 and $300,000) would experience a slight tax increase on average.
In other words, all groups will receive a boost in after-tax income. It's just that the rich would receive most of the benefit (though getting billionaires to relocate to America and (ideally) preventing them from using offshore tax havens would actually be a reasonable revenue-raising plan in my eyes; ditto with corporations and their offshore subsidiaries)
The WaPo article appears to be referring to the referring to Table 3, in particular the columns under "Tax units with tax cut or increase."
In particular, the average tax increase for certain tax units is larger than the average tax cut for other tax units. The issue with using that as a metric is that the percentage of tax units is already given - and the fact is that they still get a tax cut, contrary to what the OP states.
EDIT: The article actually refers to the (upper) middle class - those within the 80th to 95th percentiles.
And, the paper does, indeed state this, a net tax increase.
In 2018, about 12 percent of taxpayers would face a tax increase of roughly $1,800 on average. More than a third of taxpayers making between about $150,000 and $300,000 would pay more, mainly because most itemized deductions would be repealed.
In 2027, the overall average tax cut would be smaller than in 2018, increasing after-tax incomes 1.7 percent (table 3). Taxpayer groups in the bottom 80 percent of the income distribution—those making less than about $150,000—would receive average tax cuts of 0.5 percent or less of after-tax income. Taxpayers making between about $150,000 and $300,000 would on average pay about $800 more in taxes than under current law. About 80 percent of the total benefit would accrue to taxpayers in the top 1 percent, whose after-tax income would increase 8.7 percent. An alternative presentation of the distributional effects of the framework is available in appendix B.