President Obama began his official re-election campaign Saturday by asking for more time to fix America's problems and saying that voting for Mitt Romney would be a return to failed GOP policies.

"Republicans have found a nominee who will rubber-stamp their agenda," he said inside a packed Ohio State University basketball arena. "We've been through too much to turn back now."

Though the campaign officially begins today with stops in the swing states of Ohio and Virginia, the president has been in campaign mode for months, traversing the country talking about election-issue topics.

Obama visited Virginia Commonwealth University later Saturday afternoon.

In Ohio, he hit most of the major issues that have so far come to define the general election, including the economy, women's health, a college education and the U.S. military involvement overseas.

Reworking a 2008 campaign promise, Obama said he wants more citizens in the United States than anywhere else in the world to have a college degree by the end of the decade.

"A college education shouldn't be a luxury, it's an imperative," he said, recalling a recent GOP battle. "That's why I'm running for president."

Rick Santorum, when he was still a GOP candidate, called Obama a "snob" for holding such views and said the president should instead be concerned about finding ways to create jobs for the unemployed.

Obama again mentioned the death of terrorist Usama bin Laden, under his administration, saying he is "no longer a threat," and suggested that a Republican if elected might limit women's access to reproductive health care.

"I want women to make their own choices," he said to applause.

Obama also argued the recession and prolonged recovery that have largely defined his first term began under the Bush administration while he was still campaigning four years ago.

The Republican National Committee responded after the Ohio speech, by saying Americans think one Obama term was enough.

"Four years ago President Obama set the goal posts with the question of 'will this country be better off four years from now?' Four years later, a crowd of his supporters gave him the answer so many Americans agree with -- a resounding no," said committee Chairman Reince Priebus.

Obama won Ohio and Virginia in his 2008 election, and this will be at least his fourth visit this year to each of the states.

The president was joined on the campaign trial by first lady Michelle Obama, who spoke first in Ohio before the estimated crowd of 14,000.

"More than ever before Barack needs your help," she said. "He needs every single one of you to give just a little part of your life to this campaign."

No Republican has won the general election without winning Ohio, which has 18 electoral votes.

Romney -- who started his campaign last summer and is now the likely GOP presidential nominee -- has campaigned in Ohio three times in the past several weeks and is scheduled to return with a town hall-style meeting Monday in Cleveland.

The president has already attended 124 fundraisers to get money for his cause, though Saturday officially kicks off the campaign.

Though Ohio and Virginia have jobless rates below the national average, the trips come amid polls that continue to show a close race and a downbeat Labor Department report Friday that showed the jobless rate at 8.1 percent in April, but only 115,000 jobs being added that month.

The most recent poll by Quinnipiac University showed Romney ahead in Ohio , 44 percent to 42 percent, within the poll's margin of error but a significant change since the school's March poll that had Obama leading by 6 percentage points.

Quinnipiac pollsters note two significant factors on how Romney cut into the president's lead.

"Now the de facto nominee, Romney is no longer being attacked by his fellow Republicans, who are closing ranks behind him. Second, voter optimism about the economy has leveled off," they said.

The president will visit Virginia Commonwealth University for the other part of the Saturday trip, marking the second time in two days he has been in the state. Obama spoke with students Friday at a northern Virginia high school.

A Washington Post poll released this week showed Obama leading Romney in Virginia 51 percent to 44 percent, among registered voters, essentially the same numbers as a Post poll taken in April-May 2011.

Fox News Channel political analyst Dick Morris said Saturday the recent polls result are misleading because those surveyed should be un-registered voters, not likely voters.

"Obama will not get the undecided vote," he said.