Democrats mustered 51 votes for the measure to 45 against, but as expected, failed to get the 60 votes needed in the 100-member Senate to overcome a GOP filibuster threat and move forward to a full debate and vote on the bill aimed at getting more tax revenues out of the wealthy, Reuters reported.
At the White House, Obama denounced the vote, saying Republicans chose once again to protect tax breaks for the wealthiest few Americans at the expense of the middle class, Bloomberg Businessweek reported.
In a statement issued after the vote, he said he would keep pressing Congress to help the middle class. It's just plain wrong that millions of middle-class Americans pay a higher share of their income in taxes than some millionaires and billionaires, the president said.
Obama and congressional Republicans are squaring off this week over tax hikes for millionaires and a competing Republican plan to give new tax cuts for businesses.
Though scant changes to tax policy are expected ahead of the November election, the skirmishes will give voters a preview of debates they will hear over the next seven months.
I do think it is an important message for Washington to send to middle-class Americans, said Sen. Sheldon Whitehouse, D-R.I., a sponsor of the legislation. He said Democrats will keep pushing this issue all year long.
Obama and his fellow Democrats are arguing that raising taxes on the rich will help reduce deficits and bring more fairness to the tax code. Congressional Republicans are pushing a much different narrative of tax cuts - even if they add to deficits - as a way of creating jobs.
Central to Obama's tax fairness re-election campaign theme, the rule is named after billionaire Warren Buffett, who supports it and famously complains that he pays a lower effective tax rate than his secretary.
Republicans argued that raising taxes would hurt the fragile economy. Republican Sen. Susan Collins of Maine voted for the tax hike on the wealthy, while Democratic Sen. Mark Pryor of Arkansas voted against Obama's initiative.
A series of pivotal decisions on tax policy are looming at year's end, when lower tax rates for all individuals - enacted under former President George W. Bush - are set to expire. These include estate, capital gains and dividend tax rates.
Economists worry that a partisan stalemate after the presidential and congressional elections could stall action on those decisions and several other measures, hobbling the economic recovery.
Politicians' time would be better spent working on an overhaul of the tax system that could actually pass rather than reforms that are likely to go nowhere, said Maya MacGuineas, president of the non-partisan Committee for a Responsible Budget.
Republicans say the Buffett measure will do nothing to solve the larger problem of deficits and unemployment.
We have a president that seems more interested in pitting people against each other than he is in doing anything, said Senate Republican Leader Mitch McConnell of Kentucky.
He was hitting on a Republican theme that raising taxes on the rich was tantamount to class warfare.
On Thursday Republicans - in firm control the U.S. House of Representatives - are expected to debate and likely approve a bill to give a one-year, 20-percent tax deduction on business income to owners of businesses with fewer than 500 employees.
Republicans are portraying that tax cut as one for small businesses, a group they say the Buffett Rule will harm.
Democrats say the legislation will add to already huge budget deficits, since Republicans do not include any measures to offset the $46 billion revenue loss. And they cite studies showing that the tax cut will mainly go to those with incomes over $200,000 a year.
That measure is not likely to make it through the Senate.
The battle over taxes has been escalating for weeks with the White House speaking nearly daily about the Buffett Rule.
The Obama campaign played offense last week by releasing the president's tax returns several days before the deadline, to put pressure on Republican presidential candidate Mitt Romney.
Obama and his wife paid about 20.5 percent of their income in taxes in 2011, compared to an estimated 15.4 percent rate paid by the Romney's.
Romney, however, has asked for an extension to file his taxes.
A Gallup poll out on Monday said that Americans are split fairly evenly between those who say their federal tax bill is fair and those who say they pay too much.
But when asked specifically about how the wealthy are taxed, about 60 percent back some kind of Buffett Rule, Gallup's surveys have found.
It is a robust finding across whichever polls that ask, you usually get 60 percent plus that say, 'yes, higher income are paying too little,' Frank Newport, editor in chief of Gallup polling, said.
The polling, telephone interviews with about 1,000 adults, has a margin of error of 4 percentage points.