Most of the polls that I have found state that the majority supports gay marriage, not "unions like marriage" (which is oddly specific).
Poll: 55 percent support same-sex marriage
Wikipedia: Polls in 2013
That is because most polls you read leave out the companion question about redefining marriage.
Actually, the first link I supplied stated this:
"The survey also found that six in 10 Americans believe the federal government should recognize same-sex marriages performed in the states that already permit gay marriage. Of those surveyed, 39 percent say they back the Defense of Marriage Act, which prohibits the federal government from doing so."
While it may not have the religious connotations as the phrase "redefining marriage," it still deals with the same subject. It's just redefining marriage on a federal level, and not on a religious one.