He did not elaborate, but his pledge seemed designed to appeal to independents and other voters who say they are tired of seemingly perpetual campaign bickering and Washington gridlock.
But Romney said Obama's entire campaign rested on his ability to persuade people to ignore his record and listen instead to his rhetoric.
"It is not his words people have to listen to. It's his action and his record," he said in his appearance in Powell, Ohio. "And if they look at that, they'll take him out of the office and put people into the office who'll actually get America going again."
Romney's speech included an appeal to women made on economic grounds rather than on the basis of social issues like abortion, the sort of approach the Republican hopes will eat into Obama's polling advantage among female voters.
"I want to make sure that we help entrepreneurs and innovators. I want to speak to the women of America who have dreams, who begin businesses in their homes, who begin businesses out in the marketplace, who are working at various enterprises and companies," he said.
"... Our campaign is about making it easier for entrepreneurs, women and men, to start businesses, to grow businesses," Romney said. He said most jobs are created by small businesses rather than larger firms or corporations.
Romney envisioned an economic resurgence fueled by abundant energy, expanded trade and a skilled workforce. If that happens, "America is going to surprise the world. We're going to stand out as a shining city on a hill in part because of our extraordinary economy," he said to the cheers of an estimated 5,000 supporters.
Romney's determination to turn the campaign's attention to the economy follows two weeks of controversy over Medicare, courtesy of Obama's campaign, as well as abortion, the result of a comment by Rep. Todd Akin, the party's candidate in a Senate race in Missouri.
Romney joined an unsuccessful effort by party leaders to force Akin to quit his race after he said women who are raped rarely become pregnant, a view unsupported by medical evidence.
He also fought back hard in recent days in person and television advertising against Obama's allegations that he and running mate Ryan would remake Medicare in a way that would undermine the health of future seniors.
Romney's objective appears to be to erode Obama's advantage among women voters and those who say Democrats are better equipped to handle Medicare, the giant health care program for seniors.
In the AP interview, Obama said it was Romney's promises that represented the real threat to the economy and the pocketbooks of millions.
"Mitt Romney is proposing a $5 trillion tax cut that disproportionately goes to the wealthiest Americans. And he will pay for that by gutting investments in things like education, infrastructure, basic science and research, voucherizing Medicare...."
Inside the Tampa Bay Times Forum, thousands of inflated red, white and blue balloons nestled in netting high above the arena floor, ready to be dropped in the traditional convention finale on Thursday night.
Technicians tested the microphones installed for each delegation, who will sit at the foot of a vast, made-for-television podium. Teleprompters where Romney will be able to see his acceptance speech scroll by were loaded — with phrases from Abraham Lincoln's immortal Gettysburg Address, lest the words the Republican presidential contender will use to launch his fall campaign for the White House leak in advance.
AP White House Correspondent Ben Feller and Associated Press writers Steve Peoples and Philip Elliott in Ohio, and Brian Bakst and Suzette Laboy in Florida contributed to this report.
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