Under the rules of the initative, they must collect 694,354 signatures by August 6, 2009 to get it on the ballot.
Here's the text of the initiative:
"The Attorney General of California has prepared the following title and summary of the chief purpose and points of the proposed measure: SUBSTITUTES DOMESTIC PARTNERSHIP FOR MARRIAGE IN CALIFORNIA LAW. INITIATIVE CONSTITUTIONAL AMENDMENT AND STATUTE. Replaces the term 'marriage' with the term 'domestic partnership' throughout California law, but preserves the rights provided in marriage. Applies equally to all couples, regardless of sexual orientation. Repeals the provision in California’s Constitution that states only marriage between a man and a woman is valid or recognized in California. Summary of estimate by Legislative Analyst and Director of Finance of fiscal impact on state and local government: This measure would have an unknown fiscal effect on state and local governments. (09-0003.)"
Under an initiative, Californians can "directly propose and enact state laws and amendments to the California Constitution. Under the initiative process, a proposed statute or constitutional amendment must receive a specified number of valid petition signatures in order to be placed on a statewide ballot for consideration by voters."