Only 35 percent do not think the government should do this.
This comes as the Supreme Court hears oral arguments in two high-profile cases this week - California's Proposition 8 and the 1996 Defense of Marriage Act, reports CBS News.
Meanwhile, a slight majority of Americans (53 percent) thinks it should be legal for same-sex couples to marry.
Although public opinion on this topic has been consistent for the last few months, it has changed markedly from as recently as a year ago.
In May 2012, just after President Barack Obama announced his support for same sex marriage, 51 percent of Americans said it should not be legal for same-sex couples to marry.
The poll further suggests the extent to which people's views have changed. 33 percent of Americans who now think same-sex couples should be allowed to legally marry say they once held the opposite view.
Similarly, just a third of Americans now think being gay or lesbian is something people choose to be; instead, 53 percent think it is something people cannot change. Twenty years ago, Americans were divided when they were asked whether being homosexual was a choice or not.
Most Americans who think same-sex relations are wrong believe being gay or lesbian is a choice. Those who do not think same-sex relations are wrong think being gay or lesbian is something people cannot change.
This poll was conducted from March 20-24, 2013 among 1,181 adults nationwide.
--ANI (Posted on 27-03-2013)