President Obama on Tuesday renewed his public push for a “Buffett rule,” hoping that the proposal to raise taxes on millionaires will deepen distinctions with his political rivals in an election year, even if it has little chance to become law.

Appearing before thousands of students at Florida Atlantic University, Obama urged the Senate to approve the Paying a Fair Share Act, which would require anyone earning at least $1 million a year to pay at least 30 percent of his income in taxes.

“I want folks to get rich in this country. It’s wonderful when people are successful. That’s part of the American dream,” Obama told the enthusiastic crowd. “But we have to understand the share of our national income going to the top 1 percent has climbed to levels we have not seen since the 1920s. The folks benefiting from this are paying taxes at the lowest rates in 50 years. That’s wrong. That’s not fair. We have to choose the direction this country will be going in.”

The Senate is scheduled to vote Monday on the proposal, inspired by billionaire investor Warren Buffett, who has said it is unfair that he is able to use tax loopholes to pay a lower effective rate than his secretary.

Although the legislation is probably doomed in the Republican-led House even if it succeeds in the Senate, the White House believes that the bill appeals to the public’s sense of economic fairness, a theme that Obama has sought to accentuate as he ramps up his reelection campaign in a sluggish economy.

The Obama campaign has been eager to paint the president as a champion of the middle class and cast his prospective GOP challenger, former Massachusetts governor Mitt Romney, who earned a personal fortune as manager of a private-equity firm, as out of touch with ordinary Americans. Romney paid an effective tax rate of 14 percent on earnings of $42 million in 2010 and 2011, according to his tax returns.

Obama did not mention Romney by name in his remarks but did refer to him obliquely when he said “some running for a certain office who shall not be named” were doubling down on the same kind of financial policies — tax cuts for the wealthy, lax regulations — that contributed to the Great Recession.

As he did in a speech to the American Society of News Editors last week, Obama blistered the Republican House’s budget, which proposes to slash entitlements and agency spending to cut more than $5 trillion from the national debt over the next decade. The president insisted that the country must take a more balanced approach that includes investments in education, energy and health care.

“In this country, prosperity has never trickled down from the wealthy few; prosperity has always come from the bottom up,” Obama said. “This is not about a few people doing well. We want people to do well, but it is about giving everybody the chance to do well. That’s what the American dream is about.”

Republicans charged that the White House is playing pure politics, engaging in “class warfare” with the rule to win middle-class votes. They said the legislation would raise $47 billion in revenue, barely making a dent in helping pay down the burgeoning national debt of $15.6 trillion.

Gail Gitcho, communications director for Romney’s campaign, said in a statement that “President Obama is the first president in history to openly campaign for reelection on a platform of higher taxes. He has already raised taxes on millions of Americans, but he won’t stop there. He wants to raise taxes on millions more by taxing small businesses and job creators.”

Before Obama’s speech, the White House released a report that showed that the top 400 richest Americans, each of whom earned more than $110 million annually, paid an average income tax rate of 18 percent in 2008, the latest year for which data are available. That compares with an average rate of 30 percent for that group in 1995, according to the report.

Meanwhile, the middle-class rate has remained roughly constant. The middle quintile of Americans, as measured by income, paid 14 percent in taxes in 1960 and 16 percent in 2010.

White House officials said the Buffett rule would help set a “principle” for broader tax reform, although they acknowledged that the legislation, on its own, would not be an answer for deficit reduction.

“Our goal is to have a progressive tax system,” Jason Furman, deputy director of the National Economic Council, said in a conference call with reporters. He added that the Buffett rule “is the simplest, most common-sense and easiest of ideas to put in place tomorrow. We’re not trying to say it solves all our budget problems or solves all our economic problems. Certainly, we would need to do more.”

Yet perhaps signaling that the rule is as much a political gambit as a policy proposal, the Obama campaign sent an e-mail to its supporters asking them to support the bill and directing them to the campaign’s Web site.

“Not only does Mitt Romney oppose the Buffett rule, but he wants to protect special breaks and loopholes that help wealthy Americans like himself avoid paying their fair share,” Obama campaign manager Jim Messina wrote in the e-mail. “If that’s not the kind of country you want to see for the next four years, do something about it now.”