Also, regarding the possibility of a constitutional amendment forbidding same-sex marriage (like Prop 8 in California):
Lobbying began immediately for lawmakers to launch the long process of a constitutional amendment to define marriage as only between a man and a woman.(from this article, emphasis mine)
No such legislation will be approved this session in the Iowa Senate, McCoy said. Senate Democratic Leader Mike Gronstal won’t allow it, he said.
Such an amendment requires the votes of a simple majority in both the Iowa House and Iowa Senate in two consecutive sessions, followed by a passing vote of the people of Iowa.