The court in a 5 to 4 ruling struck down a key component of the 1996 Defense of Marriage Act (DOMA), which withheld federal recognition and benefits from same-sex couples who are married in states where it is legal. The poll found that 56 percent approve of the ruling "providing legally married same-sex couples with the same federal benefits given to other married couples," while 41 percent disapprove.
By a smaller margin, 51 percent to 45 percent, Americans say they approve of the court's action on a case involving same-sex marriage in California. The court did not rule directly on California's Proposition 8, which defined marriage in the state to be between one man and one woman. The justices said proponents of Prop. 8 did not have legal standing to challenge a lower court's decision that it was unconstitutional.
Gay marriages in the most populous state resumed last week.
The results are similar to those of other surveys conducted since the court's historic term ended Wednesday.
The Post-ABC poll showed a narrow majority disapproving of the court's decision on the Voting Rights Act, however. The court struck down a key section of the law that required approval from Washington before any election-law changes go into effect in some states, mostly in the South.
Asked if they approved or disapproved of the court's decision "striking down a key part of the federal law overseeing voting rights for minorities," only 33 percent approved while 51 percent answered negatively.
A poll by the Pew Research Center found different results, with slightly more people approving of the ruling than disapproving. More than four in 10 offered no opinion on the question, which did not specify whether the court upheld the law or not.
Those results underscore that public perception of the Supreme Court's work is often based on its most noteworthy decision, and this term, the issue that broke through was same-sex marriage.
According to the Pew survey, two-thirds of Americans knew that the court's rulings favored those who supported same-sex marriage. There was far less awareness of the voting rights decision.
In the Post-ABC poll, the gay-marriage decisions drew strikingly different partisan reactions, while the decision on voting rights showed a deep racial disparity.
On the question about DOMA, support for the court's decision is defined heavily by ideology, partisanship and age. The poll showed that 79 percent of self-described liberals and 68 percent of Democrats approve of the decision, while 62 percent of Republicans and 61 percent of conservatives are opposed. More than six in 10 independents and moderates approve of the decision.
The age difference was also pronounced: Two-thirds of people age 18 to 29 approve, while 56 percent of those over 65 take the opposite view.
The decision was supported in every region of the country except the South, where people were pretty evenly split.
More than two-thirds of Americans feel intensely about California gay-marriage case, and equal portions are strongly supportive of the decision on same-sex marriage and strongly opposed.
Among those who had an opinion about the voting rights decision -- a sizable 15 percent said they did not -- less than half of any racial or partisan group approved. More than seven in 10 African Americans said they disapproved of the decision, compared with less than half of whites.
The telephone poll was conducted June 26 through June 30 among a random national sample of 1,005 adults. It has a margin of sampling error of plus or minus 3.5 percentage points.
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Clement is a survey research analyst with Capital Insight, the independent polling group of Washington Post Media. Capital Insight pollsters Jon Cohen and Peyton M. Craighill contributed to this report.
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