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Low-income mothers and black parents were some of the staunchest supporters, the survey found.

A survey by the libertarian Cato Institute noted that six of the seven states that enacted tax credits for school choice programs before 2010 subsequently have voted to expand their programs. The Iowa Legislature last week overwhelmingly approved raising the cap on the state’s tax credit program from $8.75 million to $12 million and expanded the pool of corporations eligible for tax credits when they donate to scholarship organizations.

That is one reason the Republican National Committee, in its postelection analysis, said the party shouldn’t have left that arrow in its quiver in the last campaign.

“Perhaps no policy demonstrates the depth of our party’s commitment to all Americans as strongly as school choice — our promise of ‘equal opportunity in education’ to all children regardless of color, class or origin,” the RNC report said.

Former Florida Gov. Jeb Bush, who has made education reform his focus since leaving office, said school choice sends a unifying message to voters.

“Those who embrace school choice are saying they believe every parent should be able to select the school that best fits their child, regardless of their ZIP code or salary,” Mr. Bush said.

Is the issue oversold?

Democrats say Republicans are overselling the issue’s appeal in places such as New Hampshire.

“This has been a state that traditionally has been strong pro-public education,” said James M. Demers, co-chairman of President Obama’s New Hampshire campaign. “So that may be an issue that mobilizes the more conservative wing of the Republican Party, but this is another one of those issues that doesn’t play well in the general election. The independent voters, which is the biggest bloc of voters here, tend to not support that approach.”

Mr. Bush, Mr. Paul and Mr. Jindal are only a few of the potential 2016 Republican presidential candidates who are embracing school choice.

Sen. Marco Rubio of Florida is pushing a proposal that would create tax breaks for individuals and corporations that send charitable contributions to scholarship-granting organizations, which provide money to eligible students who attend private elementary and secondary schools.

Gov. Scott Walker of Wisconsin is pushing to expand the state’s school choice program by ratcheting up the amount of voucher money set aside for private and religious schools.

New Jersey Gov. Chris Christie has promoted tax-credit scholarships and called on the Legislature this year to set aside more money for scholarships that could be used to pay tuition at private schools or out-of-district public schools.

“There is nothing that angers me more than going into urban school settings, watching kids fail and looking at parents who say, ‘I have no option, governor,’” Mr. Christie said at a town-hall event in March.