President Obama on Monday called for an extension of the George W. Bush-era tax cuts for the middle class, setting up an election-year showdown with congressional Republicans and sharpening the contrast with Republican rival Mitt Romney on the crucial issues of taxes.

At an event staged in the East Room with working families, Obama announced that he would support a one-year extension for households earning less than $250,000, citing the tough economic times “when so many people are trying to get by.” But the president added that he supports allowing the tax cuts to expire at the end of the year for higher-income earners, putting him at odds with the GOP, which favors extending them for all income levels.

Obama has long advocated higher taxes for wealthier Americans, but by renewing the push four months before the election, the White House is calculating that forcing Republicans to reject the president’s proposal would put GOP lawmakers, and Romney, in a difficult position at a time when the key political questions revolve around the struggles of ordinary Americans.

“Many members of the other party believe that prosperity comes from the top down, so that if we spend trillions more on tax cuts for the wealthiest Americans, that that will somehow unleash jobs and economic growth,” Obama said. “I disagree. I think they’re wrong. I believe our prosperity has always come from an economy that’s built on a strong and growing middle class.”

The tax cuts dating to the Bush administration are set to expire for all income levels at the end of this year. And the debate over tax fairness has grown more pronounced with the looming deadline, this winter, of the “fiscal cliff” — a combination of mandatory spending cuts and tax increases agreed upon last year to tame the deficit that many economists believe could throw the country back into recession.

The White House and Congress have shown few signs of coming to an agreement to head off such a scenario. Republicans quickly denounced Obama’s latest proposal, arguing that it was an attempt to distract the public from the poor economy.

House GOP leaders have scheduled a July 23 vote on a one-year extension of the tax cuts for all income earners, and they charged that the president’s plan would raise taxes on small-business owners.

“President Obama is still asleep at the switch when it comes to our economy and jobs,” House Speaker John A. Boehner (Ohio) said Monday. “In the wake of another weak jobs report, the president is doubling down on his quixotic call for the same small-business tax hikes that have been routinely rejected by the House and Senate.”

Romney spokeswoman Andrea Saul echoed that sentiment, calling Obama’s proposal “a massive tax increase.” She added that it “proves again that the president doesn’t have a clue how to get America working again.”

Obama said his plan would cover 98 percent of the working public and 97 percent of small-business owners. Allowing the tax cuts to expire for higher-income earners, the president added, would bring additional revenue to help pay down the spiraling national debt.

Extending all the Bush tax cuts and restraining the growth of the alternative minimum tax would cost about $221 billion next year, according to the nonpartisan Congressional Budget Office. Extending the cuts only for families earning less than $250,000 would cost only slightly less — around $175 billion in 2013, according to rough CBO estimates.

Obama abandoned a similar push in 2010, when he supported a full extension of the Bush tax cuts after Republicans won a sweeping victory at the polls that fall. This time, however, White House press secretary Jay Carney said that Obama would reject any legislation that extends the tax cuts for all income levels.

“He would not support it. He would not sign that bill,” Carney said.

The president has centered his reelection campaign on a message of building a stronger middle class. He just concluded a two-day bus tour through Ohio and Pennsylvania during which he touted gains in manufacturing and the rebound of the auto industry.

The president’s message has been at times overshadowed by a series of dismal employment reports that show the economy nearly at a standstill. Last month, the economy added just 80,000 jobs, according to the Labor Department, well below the number needed just to keep up with population growth. Unemployment was unchanged at 8.2 percent.

Obama’s tax strategy could have put him in an awkward position with Democratic allies in Congress, some of whom have lobbied for tax cuts for families earning less than $1 million — a higher threshold that some Democrats believed would be more popular.

But the White House worked behind the scenes to consolidate support for the president’s proposal, according to congressional aides. Last month, Obama senior adviser David Plouffe, counselor Pete Rouse and Chief of Staff Jacob J. Lew met with several Senate Democrats, including Majority Leader Harry M. Reid (Nev.) and Charles E. Schumer (N.Y.), to discuss the tax plan.

At that meeting, Schumer withdrew objections to the $250,000 level, and the leaders agreed to support the White House, according to a Democratic aide.

Meanwhile, Treasury Secretary Timothy F. Geithner is due to address Senate Democrats at their weekly luncheon Tuesday. Aides said he is likely to discuss the economy and an impending vote on a measure to cut taxes for small businesses that hire new workers or raise wages for existing ones, as well as the president’s call for a quick vote to extend the middle-class tax cuts.

The hiring measure, proposed in Obama’s jobs bill and included more recently on his economic to-do list, was gaining momentum in the Senate, and Democratic aides said they expect to secure enough Republican support to formally open debate on it Tuesday.

Also Tuesday, the president will visit Cedar Rapids, Iowa, where he is scheduled to meet with a family that would benefit from the tax-cut extension.

Lori Montgomery contributed to this report.