(CNN) – Mitt Romney joked Tuesday about being "terribly partisan" during a question and answer session devoted to the subject of education.
Romney said as president, he wouldn't prevent teachers from going on strike, as they recently did in Chicago. But the GOP presidential nominee said he thought the influence of teachers' unions on the Democratic Party was bad for policy.
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"I don't mean to be terribly partisan, but I kind of am," Romney said, according to written pool reports.
In the session, sponsored by NBC, Romney was asked if all children in America should be afforded the type of education Romney himself received at Cranbrook, the private prep school in Michigan.
The candidate said tuition figures don't always equate with the quality of education.
"I reject the idea that everybody has to have, if you will, a Harvard-expense level degree to be successful," Romney said.
Earlier Tuesday, President Barack Obama took aim at Romney for his education policies, saying his rival was vilifying teachers.
"Governor Romney and a number of folks try to politicize the issue and do a lot of teacher-bashing. When I meet teachers all across the country, so devoted and dedicated to their kids, and what we've tried to do is actually break through this left-right, conservative – liberal gridlock," Obama said on NBC's "Today."
The two presidential candidates have long been at odds over some aspects of education policy, with Romney claiming Obama is too concerned with placating teachers' unions, which are major sources of Democratic campaign cash, and Obama saying Romney is wrong on his position that smaller class sizes aren't necessarily advantageous to better learning.
Romney reiterated that point Tuesday, saying in the education forum that neither class size nor the money spent per student was the deciding factor in a good education.
"It was the quality of teachers," Romney said, saying if he becomes president he wouldn't try to run schools from the White House.
"Mitt Romney's education rhetoric today may have sounded nice, but it doesn't square with his record or policies, which are informed by the mistaken belief that we can somehow improve our schools while cutting their budgets and laying off teachers," Lis Smith, an Obama campaign spokeswoman, wrote in a statement.
"Cutting education to pay for tax cuts for millionaires and billionaires might make sense in Mitt Romney's world, but it's not a recipe for growing the economy or strengthening the middle class," Smith added.
CNN's Kevin Liptak and Ashley Killough contributed to this report.