Twenty-eight percent think same-sex couples should be permitted to form civil unions, but more than a third - 36 percent - say there should be no legal recognition of a gay couple's relationship.
Last month, the California Supreme Court struck down that state's ban on same-sex marriage, paving the way for gay and lesbian couples to marry there.
Americans' views on this issue have changed since 2004, although opinion has not changed substantially in the last two years. In November of 2004 (soon after the presidential election) just 21 percent of Americans supported the idea of same-sex couples being allowed to marry.
Majorities of both men and women support some form of legal recognition for gay and lesbian couples, but more women (36 percent) than men (24 percent) back the idea of same-sex marriage.
More than six in 10 Democrats think same-sex couples should be allowed to either marry or form civil unions. Fifty percent of Republicans are against either of these options.
There are regional differences, too. Four in 10 of those living in the western portion of the U.S. favor same-sex marriage - the highest of any other region. Americans living in the south are least likely to support it.
Groups most likely to support same-sex marriage include those under age 30, liberals, Americans living in the west, and those who never go to church.
Republicans, conservatives, white evangelicals and weekly church attendees are groups that are least likely to support the idea.
Read The Complete CBS News Poll
This poll was conducted among a random sample of 1,038 adults nationwide, including 930 registered voters, interviewed by telephone May 30-June 3, 2008. Phone numbers were dialed from RDD samples of both standard land-lines and cell phones. The error due to sampling for results based on the entire sample could be plus or minus four percentage points. The error for subgroups is higher. The error for the sample of registered voters is plus or minus four points.