On Monday, President Obama arrived at the place that many presidents reach when a recession won’t quit: He went after the rich.

Obama said he planned to increase tax rates on the wealthy, to ensure they “pay their fair share, just like everybody else.” Republicans called Obama’s ideas “class warfare” and suggested that they would hurt the economy by leaving small-business owners with less money to spend.

Their argument sets up a replay of an old American debate occurring across a new political landscape.

Democrats remember when Franklin D. Roosevelt and Bill Clinton won their fights to make the wealthy pay more. Republicans remember when Ronald Reagan won his battle, seeking economic recovery by having the wealthy pay less.

During this go-round, the Democrats are making their pitch to a country just a few years removed from a credit bubble when millions felt newly rich.

Now, will the wealthy seem distant enough to target?

“When everybody went up, it was a lot harder to make this argument,” Sen. Charles E. Schumer (D-N.Y.) said Monday. But, he said, as the recession goes on, the argument will find more traction. “I think the time is ripe again. And I think the president sensed that.”

Arguments over the role of the wealthy in an economic recovery have always highlighted contrasting visions of the American idea. Historically, Democrats have tended to stress values such as equality and fairness — the idea that patriotism requires those who have more to do more.

“Our revenue laws have operated in many ways to the unfair advantage of the few,” Roosevelt said in a message to Congress in 1935. He wanted a wealth tax on the richest Americans in the midst of the Depression. He got it.

Clinton campaigned on a promise to raise taxes on the country’s highest bracket. After he was elected, Congress, then in Democratic hands, went along.

On Monday, as Obama outlined plans to increase tax rates on wealthy Americans, he mentioned the idea of “fairness” 11 times.

Obama said he only wants the rich to pay tax rates equal to those with lower incomes — to pay their “fair share.” What Republicans want instead, he said, was to preserve the “unfairness” of the status quo.

“It’s . . . about fairness,” the president said as he concluded. “It’s about whether we are, in fact, in this together, and we’re looking out for one another. We know what’s right. It’s time to do what’s right.”

Democratic pollsters have said that this idea — at least in theory — has wide public support. In July, a Washington Post-ABC News poll showed that 72 percent of respondents supported raising taxes on incomes of more than $250,000 a year.

“It’s a mainstream position,” said Stan Greenberg, a longtime pollster for Democrats. “It’s not divisive, but it’s in fact where the great, great majority of the country is.”

And the idea resonated among some people on the streets of Washington on Monday.

“I feel people that make more money should pay more,” said computer assistant Cheryl Grady, 52, of Logan Circle.

Grady rejected the idea that taxing the wealthy more would stifle investment or job creation. “I don’t buy that,” she said. “They get to keep more of their money, and the people who can least afford it, at least in this economy, are the ones who are really stretched.”

Republicans said Monday that Obama was guilty of class warfare by pitting the interests of most Americans against those of a small group. In addition, GOP leaders said, Obama’s plans would increase taxes on some small businesses, taking away money that could be used to hire unemployed workers.

This was their take on the American idea — that the most important values are free enterprise and independence. They said higher taxes would infringe on both.

“The point is this: It’s about jobs right now. You don’t create jobs by raising taxes. We’ve seen that,” House Majority Leader Eric Cantor (R-Va.) said at an event in Richmond on Monday, according to the Richmond Times-Dispatch.

Here, the GOP also thinks it has history on its side. Reagan, facing an economic downturn in the early 1980s, argued that the answer was to decrease taxes — for everyone, including the rich.

“Our aim is to increase our national wealth so all will have more, not just redistribute what we already have, which is just a sharing of scarcity,” Reagan said in an address to the country in 1981.

That argument still resonates with Raul Fernandez, chairman of Reston-based software firm ObjectVideo. Fernandez said he would probably be affected by the tax increases Obama proposed.

To protest them, he said, he was printing T-shirts that read “I am not Warren Buffett.” When Obama proposed the changes, he cited support from Buffett, a billionaire, who said his tax rates ought to be higher.

To Fernandez, a Republican who supported Obama in 2008, the president’s message was an undue punishment for success.

“I think it’s very easy to point to one person and very simplistically make that person personify a whole group of individuals that have created jobs and invested in the country and helped move the needle for generations,” Fernandez said.

The current round of this debate is likely to last until the 2012 election. On Monday, some historians said they thought the Democratic side was handicapped by its lead messenger.

“I think Bill Clinton felt this stuff in his bones, in a way that Obama does not. And I think Franklin Roosevelt . . . felt this in his bones in a way that Obama does not,” said David Greenberg, a history professor at Rutgers University.

While past presidents had sought to make an emotional case for the little guy, Obama chose a different tactic Monday. As he presented his case for tax increases on the wealthy in the Rose Garden, he seemed to want to divorce the debate from emotion altogether and let reason carry his argument.

“This is not class warfare,” Obama said. “It’s math.”

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