Speaking at a community college in Elyria, Ohio, Wednesday, Obama said he "wasn't born with a silver spoon in my mouth," and that he and and wife were given "a chance" by others, the Los Angeles Times reported.
During the speech, Obama also praised the school for its job training programs and said Republican budgets would cut such programs.
"I know the president likes to attack fellow Americans," Romney said in response to the "silver spoon" comment. "He's always looking for a scapegoat, particularly those who have been successful like my dad and I'm not going to rise to that. This is a time for us to solve problems."
Ohio officials are questioning Romney's decision to speak in front of a shut down drywall factory in Lorain, Ohio, Thursday, The Cleveland Plain Dealer reported.
Romney used the National Gypsum plant as a backdrop to illustrate his message that Obama has failed to create jobs.
"What we're saying is, he has been given three years to turn the economy around and bring back jobs," Romney spokesman Ryan Williams said. "He has had time and hundreds of billions of dollars to turn around the economy and he has not done that."
But Lorain locals questioned the move.
"When you have to clean up a mess that was created over eight years, you will not get it done in four," said Lorain City Council President Joel Arredondo. "After four years, we are better off than we were before."
Meanwhile, U.S. Republicans are divided over the choice of a running mate for Romney, a poll indicates.
The CNN/ORC poll found there is no consensus among Republicans and independents that lean Republican concerning the second spot on the GOP ticket.
The survey found 26 percent of those questioned would like to see former Secretary of State Condoleezza Rice as Romney's vice presidential running mate while 21 percent favored Romney's chief rival, former Sen. Rick Santorum of Pennsylvania.
When pollsters asked Tea Party supporters who they would like to see on the ticket, Rubio was first with 22 percent followed by Christie at 18 percent.
The telephone poll of 473 Republicans and independents that lean Republican was conducted by ORC International from April 13-15. The margin of error is plus or minus 4.5 percentage points.