The name of the bill is a play on the Democrats' proposed "Buffett Rule," which would set a 30 percent minimum tax rate on people earning more than $2 million per year. The Democratic proposal is a reaction to comments from billionaire investor Warren Buffett, who has said he pays a lower tax rate than his secretary.

But the Democratic proposal is also aimed partly at GOP presidential candidate Mitt Romney, whom they have noted repeatedly pays a tax rate of 15 percent or less because so much of his income comes from capital gains, which are taxed at a different rate than income.

Republicans have countered by saying tax hikes would hurt job creation, and offered a counter-proposal to let the wealthy donate as much as they like when they pay their tax bill.

"So, if Warren Buffett wants to give, then H.R. 6410 allows him to give to his heart's content, and the payments will go directly to an account at the Treasury dedicated exclusively to debt reduction," House Ways and Means Committee Chairman Dave Camp (R-Mich.) said on the House floor. "Mr. Speaker, it is not enough to speak in political platitudes about what we can do to reduce our debt. Now you can put your money where your mouth is."

Democrats opposed the bill as a ripoff of their Buffett Rule idea.

"This bill has nothing, zero, to do with the Buffett Rule," Ways and Means ranking member Sandy Levin (D-Mich.) said. "It has everything to do with the absolute refusal of Republicans to face the basic issue: that present tax laws give an inordinate tax break to the very wealthy."

The House Budget Committee's ranking member. Rep. Chris Van Hollen (D-Md.) added that by calling up the bill, Republicans were trying to "make a mockery of the real Buffett Rule."

The Senate is highly unlikely to consider the bill this week, which is the last week that both the House and Senate are expected to be in Washington.