President Obama will seek re-election vowing to rein in one of them: Wall Street. Mitt Romney will focus on the other: Washington.

Mr. Romney made that clear Tuesday night in a forceful speech claiming victory in the New Hampshire primary. Before racing to South Carolina to continue battling his Republican rivals, his remarks outlined competing visions of opportunity, fairness and blame that could polarize the 2012 election. “The president puts his faith in government,” he said. “We put our faith in the American people.”

In some ways, that’s familiar partisan boilerplate; “trust the people” was a signature phrase of Bob Dole’s unsuccessful challenge to President Bill Clinton in 1996. But the tumultuous events of the last four years have lent new resonance to the debate, even as the evolving Republican and Democratic coalitions have made it more complex.

On the Democratic side of that debate, President Obama last month blamed “you’re-on-your-own economics” for allowing corporations to seek cheaper workers overseas, hold down wages at home, exploit consumers and fuel income inequality by lavishing compensation on top executives.

He called for a 21st-century version of Theodore Roosevelt’s progressive movement that would raise taxes on the wealthy to finance job-creating improvements in infrastructure, education and scientific research. Mr. Obama’s view draws strength from voters’ antipathy toward a Wall Street culture that prospered while Main Street struggled — and then received a taxpayer bailout.

Tuesday night was Mr. Romney’s rejoinder. “The middle class has been crushed,” he declared. But drawing on controversies over economic stimulus, bailouts and health legislation, he identified a dramatically different set of villains.

Mr. Romney blamed a “bigger, more burdensome and bloated” government that racked up debt and damaged the nation’s credit rating. He attacked “job-killing regulations,” “ever-increasing government checks and cradle-to-grave assurances that government will always be the solution.”

“President Obama wants to put free enterprise on trial,” he said. “I will offer the American ideals of economic freedom a clear and unapologetic defense.”

That contrast recalls fights from earlier generations pitting business-friendly Republicans against populist Democrats. But shifts in the political landscape have blurred some of those lines, potentially complicating the general election and Mr. Romney’s upcoming primary battles in South Carolina and Florida.

Democrats have made inroads in recent elections among affluent, well-educated voters. Mr. Obama’s 2008 campaign captured the majority of voters earning more than $200,000 and raised more than $90 million from the securities, finance, hedge fund and banking industries.

Republicans have bolstered their support among the sorts of middle and working-class voters who call themselves conservative Christians and identify with the Tea Party. And in 2008 Senator John McCain got more votes among whites earning less than $50,000 than Mr. Obama.

That’s why Mr. Romney’s approach might pose a risk. A Pew Research Center survey identified financially-squeezed “disaffected” voters as a Republican-leaning constituency; just 21 percent of them agreed that “most corporations make a fair and reasonable profit.”

Those are precisely the sorts of voters that Mr. Romney’s rivals are appealing to in South Carolina’s Jan. 21 primary by attacking his career at Bain Capital. Newt Gingrich accused Mr. Romney of having “looted” companies that Bain acquired at workers’ expense; Gov. Rick Perry of Texas likened Bain to “vultures.”

Mr. Obama’s political team has offered overlapping attacks — with much more to come in the fall. And that’s why some conservatives see danger in Mr. Romney’s complaint on Tuesday night that Mr. Obama practices a “bitter politics of envy” marked by “resentment of success.”

“Careful, Mitt,” tweeted the conservative writer Ramesh Ponnuru during Mr. Romney’s speech. “Don’t want to insinuate that people only oppose you because they resent your success.”

Mr. Romney has reached out to such working-class Republicans by promising a crackdown on China’s trade practices and a tough stance against illegal immigration. He didn’t mention either in Tuesday night’s speech. But he did offer a cultural appeal reminiscent of the way another Republican patrician, George Bush, used symbols like the American flag to make patriotism a wedge issue in his 1988 presidential campaign.

“President Obama wants to fundamentally transform America,” Mr. Romney said. “We want to restore America to the founding principles that made this country great. He wants to turn America into a European-style social welfare state.  We want to ensure that we remain a free and prosperous land of opportunity.

“This president takes his inspiration from the capitals of Europe; we look to the cities and small towns of America.”

Democrats consider that formulation a device to suggest that Mr. Obama is somehow less than fully American.

Framing Mr. Obama’s goal as an “entitlement society” capitalizes on the sense of grievance among many middle-income voters that government takes their money in taxes to distribute it to others who don’t deserve it.

“There’s a bias against welfare for the poor,” said Michael Tanner of the Cato Institute. “The middle class largely believes they earned their benefits.”

Dramatic oratory aside, Messrs. Romney and Obama are seeking ways to position themselves as reasonable centrists in a general election. Mr. Obama on Wednesday announced that he will offer new business tax breaks for companies that return jobs to the United States. Mr. Romney has defended Social Security against Mr. Perry’s ideas for transforming it, and criticized Mr. Gingrich for suggesting a weakening of child labor laws.

As he straddled the divide between business and working-class Republicans in his speech on Tuesday night, Mr. Romney even echoed some of the unifying rhetoric that was Mr. Obama’s earliest political hallmark.

“In these difficult times, we cannot abandon the core values that define us as unique,” Mr. Romney said. “We are one nation, under God.”

This article has been revised to reflect the following correction:

Correction: January 14, 2012

A Political Memo article on Thursday about Mitt Romney’s speech after his New Hampshire primary victory on Tuesday quoted incorrectly from one of his comments. Referring to President Obama, Mr. Romney said, “He wants to turn America into a European-style social welfare state” — not “a European-style entitlement society,” which is how the statement was rendered in the text of the speech released by the Romney campaign.

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