Imposing a minimum tax on millionaires to ensure they don’t pay a lower tax rate than their secretaries under the so-called “Buffett Rule” promoted by President Obama would not raise enough revenue to replace the alternative minimum tax, according to a new congressional study.

The study, by the bipartisan Joint Committee on Taxation, was commissioned by Sen. Orrin Hatch, R-Utah, the ranking Republican member of the Senate Finance Committee.

Under the Obama administration’s fiscal year 2013 budget, Obama proposed the Buffett Rule, named after billionaire Warren Buffett, as a re¬placement for the alternative minimum tax. Buffett has been a high-profile supporter of raising taxes on millionaires and billionaires and wrote a New York Times editorial last year entitled “Stop Coddling the Super-Rich.” However, the billionaire investor has also been criticized because his holding company, Berkshire Hathaway, has disputed its own taxes with the Internal Revenue Service.

According to an analysis by the Joint Committee on Taxation of the “Paying a Fair Share Act of 2012” (S. 2059), the Buffett Rule would generate only $47 billion over 10 years, or less than $5 billion a year. That’s a fraction of the deficit that the Congressional Budget Office estimates at over $1 trillion for the fourth straight year, Hatch’s office noted, or the AMT, which would cost $864 billion to patch for 10 years, according to the JCT.

“The President’s so-called Buffett Rule is a dog that just won’t hunt,” Hatch said in a statement. “It was designed for no other reason than politics. There is no economic rationale for it. It would do little to bring down the debt, wouldn’t come close to getting rid of the AMT, and would make our Tax Code even more complex than it already is.”

However, it would help close some unfair tax loopholes.