CEDAR RAPIDS, Iowa — Sitting at a kitchen table here with a middle-income couple and speaking later at a community college to a buoyant crowd of 1,600 supporters, President Obama on Tuesday took his message of tax fairness to Iowa, the battleground state that propelled his first run for the presidency in 2008.

Mr. Obama said his proposal this week to extend the Bush-era tax cuts for families making up to $250,000 would allow his hosts, Jason and Ali McLaughlin, to save as much as $2,000 in taxes next year. And he drew a sharp contrast between his proposals and those of his Republican challenger, Mitt Romney, who he said supported $5 billion in tax cuts that would deepen the nation’s economic divide.

“My opponent, his allies in Congress, they sincerely believe that prosperity comes from the top down,” Mr. Obama said at Kirkwood Community College. “They believe that if we spend trillions of dollars more on tax cuts, mostly for the wealthy, that it’ll somehow create more jobs.”

“I think they’re wrong,” the president said to cheers and whoops. “We tried it their way through most of the last decade, and it didn’t work.”