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Senate Democrats today introduced legislation for the "Buffett Rule," as called for in President Obama's State of the Union address last week .

The so-called Buffett Rule, dubbed as such because of the example used by the administration that billionaire investor Warren Buffett pays a rate lower than his own secretary, would ensure that the highest-earning taxpayers pay at least a 30 percent tax rate.

Sen. Sheldon Whitehouse, D-Rhode Island, today introduced the legislation, formally called now the "Paying a Fair Share Act," today on the Senate floor.

"We should celebrate the success of people who are earning $1 million and more a year, but we really don't, particularly in this time of tight budgets and hard choices, need to subsidize that," Whitehouse said.

The legislation ensures that people with incomes exceeding  $1 million pay at least a minimum federal tax rate of 30 percent. Taxpayers earning less than $1 million would not be affected by the bill.

If a person's total income, capital gains included, is more than $1 million, he or she would calculate the taxes under the current system.  If a person's effective tax rate turns out to be greater than 30 percent, he or she would pay the 30 percent.  But if a person's effective tax rate is less than 30 percent, as with Warren Buffett's at 11 percent, then he or she would pay this fair-share tax rate.

There is a provision in the new legislation that would also for the tax to be gradually phased in for taxpayers earning between $1 million and $2 million per year so that no taxpayers face a "tax cliff" where earning an additional dollar of income increases their taxes by more than a dollar. Those between $1 million and $2 million would pay on a phased-in basis a portion of the extra tax required to get up to the 30 percent effective tax rate.

The bill faces an uphill climb with Republican opposition.

"I hope that senators on both sides of the aisle will take a good look at it," Whitehouse said. "This bill would do a lot of good things. It would simplify taxes. There is no point chasing loopholes if you know you're going to have to pay the 30 percent minimum. It will simplify that. It would discourage the exotic tax dodges that allow people to go down to 14 percent or whatever tax rates, because they know they're going to get caught at 30 percent."

The bill has not been officially scored yet by the Joint Committee on taxation, but Sen. Whitehouse estimates that it is likely to bring in between $40 billion and $50 billion a year.