CEDAR RAPIDS, Iowa — 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 on Tuesday to "compromise to help the middle class."

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

From Iowa and Colorado, two of the contested states drawing intense campaign attention, Obama and Romney fought for any advantage. While Obama was back in feel-good Iowa territory to talk taxes, Romney redirected charges that he had sent jobs overseas when he worked in private equity.

"He's run some interesting attack ads on me on that topic," Romney said of the president. "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."

The former Bain Capital executive has been under heat from within his own party over his response to relentless attacks that he shipped jobs overseas. His campaign staff made sure to distribute a newspaper story critical of Obama's own outsourcing record, loading up every press seat on the campaign plane with it.

"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.

To back up that claim, the Romney camp cited a Washington Post story that describes an ongoing trend of American jobs shifting to low-wage countries, including during Obama's presidency. The story offers a critical look at the president's progress in halting the pattern.

The rhetorical standoff on taxes and jobs did little to change the underlying narrative of a stalled economy, deadlocked Washington and tight election. Obama, running for re-election under the weight of high unemployment, has shifted to pinning blame on Romney and congressional Republicans over looming tax increases.

Obama wants a one-year extension of tax cuts for households earning less than $250,000, which would cover most taxpayers in the country. Romney supports extending the federal tax cuts, first signed by George W. Bush, for all income earners. Congress is under deadline to act by year's end or everyone's taxes go up.

"Doesn't it make sense for us to agree to keep taxes low for 98 percent of Americans who are working hard and can't afford a tax hike right now?" Obama said. "What do you normally do if you agree on 98 percent and disagree on 2 percent? Why don't you compromise to help the middle class?"

Romney saw no such agreement.

"They very idea of raising taxes on small businesses and job creators at the very time we need more jobs is the sort of thing only an extreme liberal can come up with," Romney said. He said Obama's brand of "old-style liberalism of bigger and bigger government and bigger and bigger taxes has got to end."

The economic debate played out as the Obama campaign sought to undermine Romney on a separate front, accusing him of untrustworthy secrecy.

Vice President Joe Biden launched a blistering attack on Romney's refusal to release more than one year of his personal tax returns. Romney has released his 2010 tax return and an estimate for 2011. Biden said Romney made a lie of "like father, like son" by not meeting the standards his father, George Romney, set when he released 12 years of tax returns during his 1968 presidential bid.

The candidates, meanwhile, reveled in the comfort of friendly environs.

For Obama, it was Iowa, home to the people he said "gave me a chance when nobody else would." Iowa catapulted his successful presidential bid in 2008. Yet polls in Iowa have shown Obama locked in a tight race for the state's six electoral votes, a potential warning sign.

In a private chat with a family at their house, then in remarks to supporters at a community college, and finally at an ice cream shop where he ordered up some mint chocolate chip, Obama sought to show he was like the voters who made him president – and, by contrast, the ultra-rich Romney was not.

With all the power of incumbency, Obama still casts himself as the underdog.

Fresh from Romney and Republicans collecting $106 million in June, the second straight month that Obama's campaign has been outraised, Obama said returning to Iowa reminded him of his fledgling presidential bid four years ago, "when the national press was writing us off."

"We have been outspent before. We've been counted out before," Obama said. "But through every one of my campaigns, what has always given me hope is you."

Romney, at a wide-ranging town hall event, fielded questions on a litany of issues unrelated to the economy, including gay rights and abortion, the media, gun control and prison sentences. Many of the questioners showed support for Romney and disdain for the president's policies and the media.

Yet one questioner asked why Romney didn't believe in applying principles of personal liberty to areas of private life, like the rights of gays and women; Romney responded by emphasizing that these were "tender" issues, but that he was particularly committed to protecting the life of the unborn.

___

Hunt reported from Grand Junction, Colo. AP White House Correspondent Ben Feller contributed to this report from Washington.

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