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“They’ve got folks writing $10 million checks, $20 million checks,” Mr. Obama said. “They should be contributing that to a scholarship fund to send kids to college. Instead, they are going to spend more money than we have ever seen on ads. They’re betting on the fact that you get so discouraged that you decide your vote doesn’t matter. They’re betting every single $10 million check from a wealthy donor drowns out millions of voices at the ballot box. They say, ‘Obama’s grayer now, he’s not as new and as fresh as he was in 2008, so young people aren’t going to turn out the same way.’ They’re counting on you sitting on the sidelines and letting others make the choice for you.”

The president told students repeatedly, “I need your help.”

The Romney campaign countered with data showing that since Mr. Obama took office, the average cost of in-state tuition at a four-year college has risen 25 percent, from $6,585 to $8,244. Campaign officials defended Mr. Romney’s education record as governor of Massachusetts as that of an innovator.

Mitt Romney’s education reform plan — developed by a leader with a record of innovation during his term as governor of Massachusetts — will ensure that every American student has access to a world-class education,” Virginia Gov. Bob McDonnell said in a statement. “Unlike President Obama, Mitt Romney will provide the choices students need to enroll in good schools, the information parents need to hold districts accountable, and the jobs graduates need to be successful in the global economy.”