The bill would impose a minimum 30% effective federal tax rate on those with adjusted gross incomes above $1 million, although it phases in for those making between $1 million and $2 million.
Taxpayers subject to the Buffett Rule would still get a break for charitable deductions and could count both the income and payroll taxes they paid when calculating what they would owe under the Buffett Rule.
The Buffett Rule bill itself may be dead for now, but Democrats are planning to resurrect the idea repeatedly on the campaign trail over the next six months to increase pressure on Republicans, according to Sen. Charles Schumer, a member of Senate Democratic leadership.
"We actually think we can pass something," Schumer said in a conference call Monday.
The Senate debate on Monday predictably revolved around the parties' competing notions of what defines the rich's fair share and whether the tax code is sufficiently progressive.
Obama criticized Republicans for blocking debate on the rule, saying they chose "once again to protect tax breaks for the wealthiest few Americans at the expense of the middle class."
Democratic lawmakers argued the Buffett Rule would be a step toward fairness because it would ensure that no one earning more than $1 million ends up paying a lower effective federal tax rate than anyone in the middle class.
If passed, the rule would ensure that millionaires "pay a fair share no matter what loopholes or special treatment lawmakers add to the code in the future," said Sen. Sheldon Whitehouse, a Democrat who introduced the bill.
What's more, Democrats said, the money the measure would raise -- an estimated $47 billion over 10 years if the Bush tax cuts expire, or $162 billion if the tax cuts are extended -- could be used to reduce deficits or make smart investments in the country's economy.
Republicans have characterized the Buffett Rule as a political gimmick that distracts from some of the country's biggest problems -- the need to create jobs, spur economic growth and reduce the debt.
"It [reflects] a deliberate decision to encourage new investment in the economy," Portman said.
Under the current code, a small group of millionaires and billionaires do pay a lower effective tax rate than a minority of moderate-income households.
But the Congressional Research Service notes that the Buffett Rule violations aren't as egregious as many have asserted. Using 2006 data, the CRS found the average tax rate among millionaires is almost 30% -- with about a tenth of them paying a rate higher than 35% and another tenth paying a rate below 24%.
A CNN/ORC poll conducted over the weekend found that 72% of Americans support the idea of setting a minimum tax rate for people who make more than $1 million a year. Of those, 90% of Democrats, 69% of independents and 53% of Republicans back such a millionaire tax.
Many tax policy experts are not as impressed, contending the Buffett Rule further complicates an already tangled tax code. From their perspective, there are simpler and more efficient ways to raise the tax burden on the very wealthy than adding what is in essence a second alternative minimum tax to ensure the rich pay their fair share, however one defines it.
The Buffett Rule is named after billionaire Warren Buffett, who has famously claimed he pays a lower effective tax rate than his secretary and who has urged Congress to tax the uber-rich more.--CNN's Ted Barrett contributed to this report.