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The shift helps explains several recent political trends, from the rising acceptance of gay marriage, especially among younger Americans, to the popularity of President Barack Obama's proposals to raise taxes on the most affluent Americans to help finance benefits for middle-class families.
The survey shows Republicans on the wrong side of those trends, with poll respondents by two to one margins expressing disagreement with the party's approach to "social and cultural issues" and to "looking out for the middle class."
(Read More: Obama's Budget Plan Pursues These Two Goals)
On specific issues, 84 percent of American adults called "pressures to make ends meet" a serious problem. By comparison, 63 percent said that about the rise of single-parent households, 55 percent about "the declining role of religion," 54 percent about violence entertainment programs and games, and 51 percent about "putting career ahead of family."
The survey also tested reaction to some of the social and cultural changes that have affected family earnings and economic patterns. Two-thirds of adults said the changes in American life caused by more women working outside the home have been worth making, with little difference in responses between men and women.
Large majorities of men and women alike said that women are generally paid less than men for doing the same kinds of work. Strong majorities of men and women also agreed the country would be better off with more women in senior business management jobs.
(Read More: One Billion Women to Enter Workplace in Next Decade: Report)
Asked if they had personally experienced discrimination, 46 percent of women surveyed said yes, while 53 percent said no. Of those indicating they had experienced discrimination, 35 percent said that had occurred in their workplace, 15 percent it took place in a social setting, 14 percent while shopping, and 6 percent at a bank or financial institution.
On same-sex marriage, the poll measured the astonishingly rapid shift in attitudes since Republicans wielded their opposition as a weapon in the 2004 presidential campaign. That year, a NBC/WSJ poll found at the time, opponents outnumbered supporters by two to one, 62 percent to 30 percent.
Today, 53 percent of adults favor gay marriage, while 42 percent oppose it. One factor in that shift: 79 percent now say they personally know someone who is gay or lesbian, up from 62 percent in 2004.
(Read More: Corporate Call for Change in Gay Marriage Case)
The telephone poll of 1,000 adults, conducted April 5-8, carries a margin for error of 3.1 percentage points.
—By CNBC's John Harwood; Follow him on Twitter: