Romney also has cited as a model the aggressive education overhaul in Louisiana. Under Republican Governor Bobby Jindal, the state has laid out a plan to shift tax dollars from public schools to private-sector entrepreneurs and industry trade groups that design courses for K-12 students.

Romney argues that the public school system is broken and in desperate need of new ideas and new energy from the private sector. He is clear about whom he believes is to blame: A campaign policy paper calls public education "an antiquated system controlled to a disturbing degree by the unions representing teachers."

Teachers unions, predictably, have rallied to the Democratic president. They dislike some of his policies, such as his push to rate teachers largely by their students' progress on standardized tests. Still, they are expected to spend millions supporting his campaign.

"Do we believe that this administration has put too much of a focus on testing and competition? Yes," Randi Weingarten, president of the American Federation of Teachers, told a recent union convention.

But Weingarten also credited the president's stimulus bill with saving the jobs of 300,000 school employees across the nation. More recently, Obama requested - but failed to get - $55 billion from Congress to prevent some 320,000 teacher layoffs and repair crumbling schools.

For-profit colleges

In higher education, the candidates are sharply divided over the value of private, for-profit colleges that offer career training and degree programs in everything from dental hygiene to wind turbine repair to video game art.

Romney has touted for-profit colleges as vital players in higher education. Their very presence, he argues, spurs competition, keeps costs down and expands access to higher education for millions of young adults and mid-career workers looking to shift to a new field.

Obama, however, has accused the industry of promising too much and delivering too little. Too often, he says, recruiters enroll students who do not have a realistic chance of getting a degree or landing a job in their chosen field - and who gain little from the programs except mountains of debt.

In a speech to veterans this spring, Obama accused private, for-profit colleges of trying to "hoodwink" and "swindle" military families eligible for financial aid under the G.I. Bill.

The administration has sought to crack down on abuses by pulling federal aid from colleges that fail to produce enough graduates who find "gainful employment." A federal judge last month invalidated part of that regulation; the administration is still considering its response.

Romney has said he would repeal the regulation altogether.

Romney advisers say he also would push for repeal of a federal law that aims to ensure that for-profit colleges do not get all their revenue from federal student loans, but attract at least some students willing to pay the tuition out of pocket.

Calling for-profit colleges a good deal for students, Romney has campaigned several times on their campuses. Industry leaders have contributed heavily to his campaign. Bill Heavener, the CEO of Full Sail University, a for-profit college in Florida, is a top Romney fundraiser and donor.

The industry's trepidation about Obama comes through in a recent poll of influential players in the education world conducted by Whiteboard Advisors, a consulting firm.

Asked how concerned for-profit colleges should be about a second Obama term, 38 percent expressed strong concern - and another 21 percent checked the box labeled "Panic!"