WASHINGTON (AP) — A bill designed to enact President Barack Obama's plan for a "Buffett rule" tax on the wealthy would rake in just $31 billion over the next 11 years, according to an estimate by Congress' official tax analysts obtained by The Associated Press.

That figure would be a drop in the bucket of the over $7 trillion in federal budget deficits projected during that period. It is also miniscule compared to the many hundreds of billions it would cost to repeal the alternative minimum tax, which Obama's budget last month said he would replace with the Buffett rule tax.

The alternative minimum tax, originally aimed at ensuring that wealthy Americans pay taxes despite deductions and other breaks, has begun affecting upper middle-class families. Congress acts every year to minimize its impact.

The Buffett rule has become a leading symbol of Obama's and congressional Democrats' election-year efforts to persuade voters that they are the party championing economic fairness. Republicans have mocked it as one aimed at scoring political points that would have little real budgetary impact.

The plan is named for billionaire investor Warren Buffett, who has said taxes on the rich are too low. Obama has proposed requiring that people earning at least $1 million annually pay at least 30 percent of their income in taxes, but has provided few details.

In an analysis provided to The AP on Tuesday, Congress' Joint Committee on Taxation estimated that a bill introduced last month by Sen. Sheldon Whitehouse, D-R.I., attempting to enshrine Obama's proposal into law would collect $31 billion through 2022. The measure has little chance of advancing soon, especially before the November elections.

"Now that we have this analysis, I hope the president will stop the class warfare and start leading by putting out real proposals to bring down our debt, get rid of the AMT and reform our broken tax code," Sen. Orrin Hatch of Utah, top Republican on the Senate Finance Committee, said in a written statement, using the alternative minimum tax's acronym.

Hatch's Finance committee GOP aides requested the study.

Whitehouse said other groups, including the respected bipartisan Tax Policy Center, have estimated that the proposal could earn more than $31 billion.

"No matter how you slice it, that's real money that could help bring down our deficit. Most important: It's simply the right thing to do," he said in a statement.

Whitehouse's bill would require people making at least $2 million a year pay at least 30 percent of their earnings in taxes, though they could deduct certain amounts for their charitable contributions. The tax would be phased in for people earning at least $1 million annually.