CEDAR RAPIDS, Iowa (AP) - Clashing over the economy, President Barack Obama challenged Mitt Romney to join him in allowing tax hikes for rich Americans like them, needling his Republican rival to "compromise to help the middle class."

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Romney dismissed the idea and returned fire on a tender topic, calling Obama the real "outsourcer-in-chief."

From Iowa and Colorado, two of the competitive states drawing nearly all of this year's campaign attention, Obama and Romney fought for stronger footing Tuesday.

While Obama was back in his feel-good Iowa ground to talk taxes, Romney responded to charges that he sent jobs overseas when he worked in private equity.

"It is interesting that when it comes to outsourcing that this president has been outsourcing a good deal of American jobs himself, by putting money into energy companies that end up making their products outside the United States," Romney told a supportive audience.

For days, the former Bain Capital executive has been under heat from conservatives from what critics view as a failure to respond to the Obama team's attacks that Romney moved jobs out of America as he made a fortune.

"If there's an outsourcer-in-chief, it's the president of the United States, not the guy who's running to replace him," Romney said in Grand Junction, Colo.

His team sought to make clear Romney had weighed in, even loading up press seats on the campaign plane with a newspaper story critical of Obama's outsourcing record.