Like the unaffiliated, Latino and African-American voters traditionally have lower turnout rates, said Robert Jones, a poll co-author who founded the institute.
"Romney has a turnout advantage in that his supporters are more white," Jones said.
The poll showed Romney with a 21-point lead among white working-class voters overall, but the group was more divided when looked at by faith.
Sixty-six percent of white working-class Protestant voters supported Romney, compared with 30 percent for Obama. Among white working-class Catholics, neither candidate had a statistically significant edge.
The poll also laid out other voting gaps. According to PRRI, 53 percent of female voters were likely to support Obama, compared with 44 percent for Romney. Seventy-six percent of women who have never been married support Obama, while 55 percent of married women support Romney.
Issues related to reproductive freedoms, including the contraception mandate, have figured prominently in the campaign. Fifty-six percent of Americans say religiously affiliated hospitals and colleges should be required to provide no-cost contraception coverage to employees, and 45 percent said even houses of worship should be required to do so as well.
The White House mandate exempts houses of worship, but bishops and many other religious liberty advocates have said the exemption should be wider.
The poll shows Americans are divided by faith identity even on the question of what America's core problems are.
PRRI asked if the country's woes are primarily because of an unfair economic system, and then asked if they are also caused by a moral decline and the loss of traditional values. White evangelical Protestants were much more likely to identify moral decline, not economic inequality (37 percent to 5 percent). White Catholics, white mainline Protestants and Hispanic Catholics also were more likely to blame shifting values. But black Protestants and the religiously unaffiliated were equally likely to blame both factors.