Twenty-seven members of the Assembly's Republican caucus sent Schwarzenegger a letter Tuesday saying it was up to the governor to defend the rights of voters who passed Proposition 8 almost two years ago.
Chief U.S. District Judge Vaughn Walker overturned the voter-approved measure as unconstitutional last month.
The state has until Sept. 11 to challenge Walker's ruling in the 9th U.S. Circuit Court of Appeals.
Schwarzenegger and Attorney General Jerry Brown, who both refused to support Proposition 8 in Walker's court, have said they do not plan to appeal the ruling.
The coalition that sponsored the ban is appealing the ruling.