A top official with Congress's tax scorekeeper said Monday that the House Republicans' tax bill doesn't adhere to the so-called Mnuchin rule that there be no net benefit for the wealthy.

"I would say not," Joint Committee on Taxation chief of staff Thomas Barthold said during the House Ways and Means Committee's markup of the bill. "As has been pointed out it provides for net tax reductions, particularly in the first year, up and down the income distribution."

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Treasury Secretary Steven Mnuchin Steven Terner MnuchinLawmakers fear voter backlash over failure to reach COVID-19 relief deal United Airlines, unions call for six-month extension of government aid House Democrats plan to unveil bill next week to avert shutdown MORE said in a CNBC interview in November 2016 that "there will be no absolute tax cut for the upper class."

More recently, Mnuchin has backed off from that pledge, saying that it's hard to not cut taxes for the wealthy if you're cutting taxes across the board.

Barthold spoke about the Mnuchin rule in response to a question from Rep. Brian Higgins Brian HigginsBiden slams Trump for promoting conspiracy theory about man shoved by police Trump claims 75-year-old man shoved by Buffalo police could be part of 'set up' NY, NJ lawmakers call for more aid to help fight coronavirus MORE (D-N.Y.).

Higgins said that because the bill would cut taxes for high earners, "this tax plan is blatant fraud being perpetrated against Middle America."

The tax bill faced day one of a House Ways and Means Committee markup on Monday. The markup is expected to continue for several days with Committee Chairman Kevin Brady Kevin Patrick BradyBusinesses, states pass on Trump payroll tax deferral Trump order on drug prices faces long road to finish line On The Money: US deficit hits trillion amid pandemic | McConnell: Chance for relief deal 'doesn't look that good' | House employees won't have payroll taxes deferred MORE (R-Texas) indicating he expects to be done with the bill by Thursday.