The CNN poll also found that some of the cases coming before Court could again redefine voters' attitudes.

On same-sex marriage, 55 percent support allowing gays to wed, with 44 percent opposed.

Six in 10 say the federal government should recognize gay marriages in states where the practice is already legal, with 39 percent saying they disagree. The Court is expected to rule on both issues in the coming weeks.

Voters are more divided on whether the Voting Rights Act is still necessary, ahead of the court's ruling on whether the Department of Justice should still be allowed to "pre-clear" changes to voting laws in counties and states with a history of racial discrimination.

Of those surveyed, 50 percent said the civil rights legislation was no longer needed, while 48 percent said that it was.

The court is also expected to rule on a case in which a white woman in Texas sued the state's flagship university after she was rejected admission, arguing affirmative action kept her from getting in.

According to the poll, nearly seven in 10 Americans disapprove of affirmative action, despite nearly half of all Democrats and 51 percent of non-whites backing the practice.