Prop 13 represents a ceiling of 1% of assessed valuation for property tax; property taxes go to the counties, not to the state. Property tax doesn't figure into the state budget crisis ...
That being said, I've never heard of such a movement, but California property taxes are plenty high despite Prop 13 ... real estate values in the state have surged, in part due to the mid-90s boom, in part due to the supply/demand presented by millions of people flocking to the state. On a percentage basis, I have low-ish taxes (around 1.3% of assessed valuation in Oakland: the .3% is from voter-authorized bonds). But on a real dollar basis, I dare you to compare :-)
Also: California has one (if not the?) highest income tax in the nation. I know I paid a lot in tax when I lived in NYC, but it was the cumulative effect of state plus city taxes that made me approach 10% of gross ... California is around 9%.
General FAQ on the California Budget: http://www.dof.ca.gov/HTML/BUD_DOCS/question.htm Revenue Estimates, including some good analysis: http://www.dof.ca.gov/HTML/Budget02-03/15_revenue.pdf