Under California law, the Legislature writes the budget. The Governor can only recommend what the budget should look like, but lawmakers can ignore his recommendations and do whatever they please. While the Governor does have the ability to either reject all of the budget passed by the Legislature, accept all of it, or line-item veto some of it, the first option is hardly ever exercised because it takes the unusual and difficult-to-get two-thirds majority of the Legislature to pass a budget in the first place. The line-item veto only allows the Governor to dictate what dollars shouldn't be spent on, not on what they should be spent. The voters of California actually have more power than both the Governor and the Legislature to dictate what dollars should be spent on through the use of ballot initiatives. And this power often has a substantial impact on the budget. For example, Proposition 98, which guarantees minimum spending levels and annual increases thereto for public education, now accounts for 30% of spending from the General Fund. Which means that before the Legislature and Governor can even consider their first budgetary move, the voters of California have already determined how a third of the annual budget gets spent. And this spending is beyond the reach of the Governor's line-item veto. There are similar Propositions which have been passed with similar impacts on the budget. All this amounts to a system in which the Governor has little to no control over the State's budget allocations.

All this has nothing to do with whether or not there's a republican form of government but, FYI, there is.