As they head into the 2012 campaign, Democrats are changing their definition of what it means to be rich. Forget about families making $250,000 a year. Today, the party is only interested in millionaires.

In speeches across the country, President Obama has vigorously demanded that “millionaires and billionaires” pay “their fair share” in taxes. Last month, the White House said tax reform should ensure that billionaires such as Warren Buffett pay at least as much of their income to the Internal Revenue Service as middle-class taxpayers do.

And on Wednesday came clear evidence of this shift: Senate Democratic leaders scrapped Obama’s proposal to cover the cost of his jobs bill by raising taxes on income over $250,000 a year, the old Democratic standard for defining the wealthy. Instead, they are proposing a 5.6 percent surtax on annual income of more than $1 million.

Democrats say their new focus is intended to bolster support for Obama’s jobs package. But its more important purpose is to clarify the party’s economic agenda heading into next year’s election.

Democrats have long argued that, in addition to cutting government spending, lawmakers should ask people at the top of the income spectrum to pay more in taxes to help tame the national debt. But setting the dividing line at $250,000, as Obama did during the 2008 campaign, “fuzzies the picture,” said Sen. Charles E. Schumer (D-N.Y.), the leading architect of the surtax proposal. “There are lots of people who either make $250,000 or are close” to it, Schumer said, particularly small-business owners and dual-income couples living in high-cost urban areas.

“If we’re able to draw a very clear line — people above a million dollars should pay their fair share — it’s much easier to win that argument,” said Schumer, who is also in charge of political messaging for Democrats hoping to maintain control of the Senate. “And I think we’re winning it. For the first time since Ronald Reagan, we’re beginning to turn the tax debate around.”

Republicans scoffed Wednesday at the ploy, which Democrats acknowledge is unlikely to succeed in its immediate goal of rallying support for Obama’s $447 billion jobs package. Several Democrats, including Sen. Joe Manchin (D-W.Va.), oppose increased spending in the bill at least as much as the tax hikes Obama urged as a way of covering the cost. No Republican is likely to vote for the measure, making it impossible for Senate Majority Leader Harry M. Reid (D-Nev.) to muster the 60 votes needed to avert a filibuster when he opens debate on the bill as soon as next week.

Senate Minority Leader Mitch McConnell (R-Ky.) accused Democratic leaders of reworking the bill “not to grow bipartisan support” but “to sharpen its political edge.” Michael Steel, a spokesman for House Speaker John A. Boehner (R-Ohio), said Democrats should focus on identifying “areas of common ground” with Republicans “to create a better environment for job creation” instead of floating “desperate tax-hike gimmicks . . . to cover up divisions within the Democratic caucus.”

GOP claims that there is more style than substance to the surtax gained support late Wednesday when Democrats abruptly upped the proposed levy to 5.6 percent from the 5 percent offered earlier in the day. After reporters peppered White House press secretary Jay Carney with questions about the wisdom of imposing the tax in January 2012, when the economy is likely to still be weak, Senate Democrats pushed the implementation date back a year. But that required raising the rate to ensure that the surtax generates enough cash over the next decade to cover the full 10-year cost of the jobs bill.

Still, polls show Democrats may be on to something. In a new Washington Post/ABC News survey, 75 percent of those polled said they support raising taxes on millionaires, including 57 percent of Republicans.

Republicans still hold an advantage on the tax issue, with 49 percent of those surveyed saying they trust Republicans to do a better job of handling taxes, compared with 39 percent who trust Obama — a 12-percentage-point swing toward the GOP since April. But Senate Democrats believe they now have a crisper message to carry to the voters and into debt-reduction talks this fall on Capitol Hill.

“If we can affect the tax debate by drawing this line, we make it easier to get a grand compromise on deficit reduction,” Schumer said, because Republicans’ opposition to tax hikes of any kind “will no longer be the political high ground.”

The White House on Wednesday offered support for the Senate’s surtax plan, which would apply to investment income as well as wages and inherited wealth, pushing the top income tax rate to 40.6 percent in 2013 or to 45.2 percent if the George W. Bush-era tax cuts expire on schedule that year. It would replace a raft of tax hikes offered by the White House, the largest of which would have limited the value of itemized deductions for families earning more than $250,000 a year.

House Democrats, meanwhile, are reassessing their position on who is most deserving of higher taxes.

Rep. Sander M. Levin (Mich.), the senior Democrat on the House Ways and Means Committee, said ending the Bush tax cuts for families earning more than $250,000, as Obama pledged to do during the 2008 campaign, would generate about $39 billion a year. But the vast majority of that money — 79 percent, according to the nonpartisan Joint Committee on Taxation — would come from the 315,000 households that earn more than $1 million a year, the richest 0.2 percent of taxpayers.

Those taxpayers’ incomes have risen sharply over the past three decades, Levin said — far more rapidly than households making closer to $250,000 or $300,000. Those families are well off by national standards, Levin said, but hardly rank among the super-rich.

“There’s a reason to focus in on income over $1 million,” Levin said. In the battle for more revenue, he said, “if you can’t do that, you won’t do anything.”

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