Larry Lindsey, president of The Lindsey Group and former economic advisor to George W. Bush, accuses the Joint Committee on Taxation of "playing games" to thwart the tax bill. In a client note obtained by CNBC, Lindsey characterizes the committee's scoring model as a "black box" and calls its economic assumptions on the bill "absurd."

Earlier this week, the JCT's congressional analysis showed that the Senate tax bill would fall $1 trillion short of paying for itself, even after factoring in economic growth. The report undercut the White House argument that tax reductions would effectively pay for themselves. The Trump administration and other Republicans have argued that economic growth sparked by cuts will cancel out lost revenue.

Lindsey, who also served as a Federal Reserve governor in the '90s, said because the parameters of the JCT's model have never been made public and cannot be scrutinized, the committee has unbridled power.

"In effect, the results of the model are just what the staff decides they are since they are the ones in control of the parameters of the model," Lindsey wrote. "The staff uses the artifice of a black box model to come to whatever conclusion they want."

He called the JCT's prediction of an "aggressive" Fed response to the tax legislation "absurd" and says it contradicts the Fed.

"If anything, the signals and market view have all been that the Fed will be less aggressive. Some members have even speculated about the advantage of raising the inflation target in order to allow a slower response," Lindsey wrote. "Markets have consistently priced in far fewer interest rate hikes than what the FOMC projects."

The Bush tax-cut architect ended his note by saying the JCT "has long been part of the swamp" and calling on Congress to reform the committee "when their model is proved to be a fraud."

In appearances on CNBC and in a previous note, Lindsey told his clients that if tax reform was passed, "The political and economic policy implications would be massive and far reaching."

The JCT did not respond to a request for comment.