The chief of staff to the Governor of California, Susan Kennedy, is facing calls for her to resign after Mr Schwarzenegger said he would veto same-sex marriage legislation.
Robin Tyler, a lesbian activist and plaintiff in a same-gender marriage test case to be heard before the California Supreme Court, said that she was “disappointed” in Ms Kennedy, who “married” her lesbian partner in Hawaii several years ago.
On Monday Governor Schwarzenegger announced that he would continue to block same-sex marriage legislation unless a state-wide vote overturned Proposition 22, passed in 2000 with 61% support.
Ms Tyler and her partner are one of the 15 gay and lesbian couples challenging the law before Supreme Court.
Their case is expected to be heard later this year or in early 2008.
A court subsequently ruled that Proposition 22 only bars recognition of same-sex marriages performed outside California, but the Governor insists that the people voted to ban gay marriage within the state.
“It would be wrong for the people to vote for something and for me to then overturn it,” Schwarzenegger said.
“Since I attended Susan’s wedding, why is she so against attending mine?” Ms Tyler said in a press release.
“Both Arnold and Susan know that it is unconstitutional for the majority to deny a minority equal protection under the law. To hide behind Proposition 22 as an excuse, is cowardly and unforgivable, for both the Governor and especially for Ms. Kennedy, a lesbian.
“Rather then backing the Governor’s decision with unacceptable excuses, I ask that Ms. Kennedy resign as Chief of Staff. If not, shame on you Susan, to side against your community, and deny civil marriage to your friends.”
Susan Kennedy was a controversial choice among conservatives when she became Governor Schwarzenegger’s chief of staff in January 2006.
She previously served as a Cabinet member under Democrat Governor Gray Davis.
Thousands of people protested the Governor’s decision in towns and cities across California last night.