The biggest change in the stimulus brought about by the Senate compromise bill is the removal of $40 billion in "fiscal stabilization" aid to state and local governments, and the addition of a $15,000 homebuyer tax credit that will likely cost around $40 billion. This "swap" will have a big impact on California.
California's share of the "fiscal stabilization" cut will be about $5 billion. The result will probably be deeper cuts in education funding or a state tax increase such as the temporary sales tax increase or an income tax surcharge.
A significant share of the homebuyer tax credit will also flow to California. However, I don't believe this will do much to stabilize the housing market. It will mostly be a windfall to homebuyers with solid finances (it can't help with a downpayment since the cash comes in a tax refund next year). It won't stall foreclosures, and as a temporary measure, will not have any impact on long-term home prices. Hasn't the real estate boom and bust in this state already done enough to enrich some while impoverishing others?
I recommend the state take the federal tax credit back with a surcharge on the state income tax of anyone who gets the federal homebuyer credit. I don't know the logistics and legalities of doing this, but there must be a way. It won't eliminate the need for tough choices in the state budget, but is far better than some of the alternatives being considered now like increasing the sales tax.
Update 2/13: It appears that this homebuyer tax credit has been removed from the final stimulus package, so this proposal is no longer relevant.