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The line earned a quick rebuke from the Republican National Committee, which argued that Mr. Obama was trying to move the goal posts and sent out a release highlighting his remarks four years ago when he said the “real question” was “will this country be better off four years from now.”

“Even though Obama would like us to forget he’s been president for the past three years, Americans aren’t satisfied with the Obama policies that have resulted in 12.5 million Americans unemployed, 5.5 million mortgages in foreclosure or delinquent, and a record $5 trillion added to the debt,” said RNC Chairman Reince Priebus.

Mr. Obama also took credit for ending the war in Iraq, killing Osama bin Laden, decimating al Qaeda and achieving a 2014 exit strategy for Afghanistan.

Because of the “courage and selflessness” of the military, he pledged to protect veterans and help them transition back into the economy when they return from overseas.

In a defiant defense of his signature 2010 health care law, which is under Supreme Court review, Mr. Obama said 2.5 million young people can now stay on their parents’ insurance, insurance companies can’t kick people out for pre-existing conditions and can’t charge women differently from men.

“We can’t afford to spend the next four years going backward,” he said. “America does not need to fight the battles we just had on Wall Street reform and health care reform.”

In the last four years, gay Americans no longer have to live in fear of being kicked out the military because of “who you are and who you love,” women’s right to an abortion and affordable contraception aren’t threatened and children born to illegal immigrants still have instant citizenship, he added.

“This country is at its best when we harness the God-given talents of every individual striving for the same dream.”

Mr. Obama also teed up a string of attack lines against Mr. Romney that play into attempts to characterize him as an advocate for the corporate elite.

“I don’t care how many times you try to explain it, corporations aren’t people. People are people,” he said, referring to a legal argument Mr. Romney made last year which Democrats seized on as emblematic a bias towards businesses and the free market.

“We measure prosperity, not just by our total GDP, not just by how many billionaires we produce, but by how well a typical family is doing, how far they will go on their hard work and dreams,” Mr. Obama told the crowd.