The Pew Research Center said many in this group are more welcoming about other social changes, including couples having children without marriage and gay couples raising children. The poll also asked 2,691 people about attitudes toward interracial relationships, unmarried couples living together, mothers with young children going out to work and women not having children.
Researchers said the respondents fell into three rough groups -- acceptors, rejecters and skeptics. Acceptors were 31 percent and welcome most non-traditional family arrangements, while rejecters, 32 percent, take the opposite view.
Skeptics were the largest group, at 37 percent. They tended to accept most non-traditional arrangements except single motherhood, although they were less embracing than the acceptors.
Rich Morin, a Pew senior editor and author of the report, told The Washington Post the skeptics' view of single motherhood may be rooted in experience.
"We see gay and lesbian couples raising children in loving environments," he said. "We see young mothers going off to work and coming home to raise happy, well-adjusted children. Then we see the sometimes tragic consequences of single parenthood, with just one person juggling so many roles."