The state Senate rejected a plan Friday to extend recent tax hikes for another year. The higher tax rates are set to expire at the end of the month.
Democrats say schools desperately need that money, while Republicans say extending the hike would cripple the state's economic recovery.
Gov. Jerry Brown wants to call a special election in September so voters can decide on whether to extend the hikes for five years.
The cumulative effect of those tax hikes is $260 a year on a per capita basis.
The Senate passed a few relatively minor budget bills early on Saturday but did not touch the tax question.
While senators could be called back into session this weekend, the Senate is not expected to meet again until Monday, when the Assembly also has scheduled its next floor session. That's just two days before the June 15 constitutional deadline for the Legislature to send a balanced budget to the governor.
The Associated Press contributed to this report.