The move will make some voters more likely to vote Republican in the upcoming midterm elections, but will drive others to Democrat candidates, according to the survey.
The remaining respondents said the decision, which struck down the court's 1973 decision that declared access to abortion was a constitutional right despite not being mentioned in the Constitution, will have no effect on how they vote in the midterms.
Presidential elections are held every four years; the elections held in between them are known as midterms. Along with featuring all members of the U.S. House of Representatives, voters will choose some U.S. senators and many state lawmakers and other politicians.
The Harvard–Harris poll was conducted on June 28 and June 29 among 1,308 registered voters. The margin of error and breakdown of party affiliations were not provided.
Democrats are much more likely to support easy access to abortion and few, if any, restrictions on getting or performing abortions. Republicans are largely in favor of restricting or outright banning abortion. In some cases, GOP lawmakers support criminal penalties for health care workers who perform abortions in violation of state laws.
Another recent poll indicated that Democrats may have more to gain from the Supreme Court's ruling.
The poll was conducted on June 24 and June 25 among 941 U.S. adults, including 868 registered voters. The margin of error was plus/minus 4.9 percent, or 5.1 percent for the voter subset.
Respondents to both polls were more likely to oppose the Supreme Court decision.
Fifty-five percent of respondents, including majorities of Democrats and independents, to the Harvard poll were opposed, compared to 45 percent in support. But 72 percent of respondents said they supported either a total abortion ban with exceptions for rape or incest, a ban after six weeks, or a ban after 15 weeks.
Among respondents to the other poll, 56 percent opposed the decision, versus 40 percent who supported it.