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Raul Gonzalez, director of legislative affairs for the National Council of La Raza, the largest umbrella organization for Hispanic groups, said Hispanics do consider education to be a major civil rights issue and that Mr. Romney’s push for vouchers likely will play well.

Still, he said, other than Mr. Romney’s push for school choice, and Mr. Obama’s Race to the Top program that rewards innovative schools, the two men share many similarities on education. Both favor moving away from some of the accountability provisions in Mr. Bush’s No Child Left Behind legislation, and have stressed teacher effectiveness as a solution for poor schools.

Mr. Gonzalez said there’s plenty of room for both men to have a more detailed discussion of education. He said he will be looking to see whether Mr. Romney pushes reforms that make it easier for communities to start charter schools.

Possibly the biggest difference between Mr. Obama and Mr. Romney is on the District’s Opportunity Scholarship Program, which offers federal taxpayer-funded vouchers to low-income students.

It has been contentious from the time it started a decade ago, with the powerful teachers unions opposing it but city parents in support.

As of this year, more than 1,600 students are enrolled in the program, which offers scholarships of up to $8,000 through eighth grade and $12,000 for ninth through 12th grades. The money goes to pay tuition at private schools, including religiously affiliated schools.

Mr. Obama tried to end the program when he took office, but eventually reached a compromise that let students already in the program continue, but halted new applications.

When Republicans took control of the House last year, Speaker John A. Boehner fought to restart the program, and insisted that funding be included in spending bills.

But the program remains on edge, and Mr. Obama’s 2013 budget, submitted in January, doesn’t include any money for it going forward. His administration argues that it has enough money to cover students for the next year.

Mr. Boehner, Ohio Republican, and Sen. Joe Lieberman, Connecticut independent, questioned Mr. Obama’s decision, and Mr. Boehner has vowed to demand that the program be funded.