The court released five rulings on Monday, but did not take up Prop 8 or the federal Defense of Marriage Act (DOMA).
The court added Tuesday as an extra opinion-release day. Six cases remained undecided.
A ruling on Prop 8 was expected by Friday, when the court goes on recces for the summer.
If the justices uphold Prop 8, the ban on same-sex marriage in California would remain in place.
It would also send a strong message to about three dozen other states across the country that their bans on same-sex marriage would also be found constitutional.
If the ban is upheld, it would likely trigger a political campaign in California to put the issue back on the ballot, according to experts.
Voters approved Prop 8 back in 2008, but recent polls suggest that the majority of California voters now support same-sex marriage.
If the court strikes down Prop 8, gay marriages could begin in California by mid-July, officials said.
The Supreme Court was also expected to rule on the Defense of Marriage Act, which denies federal benefits to legally married same-sex couples.
Gay marriage is legal in 12 states, as well as the District of Columbia.