I posed this question to Freditor_G a few weeks ago and this was his reply:

As a law student, I don't think there's any significant Constitutional objection to the proposal.

First, the plain language of the Constitution only says legislatures have to direct the manner in which electors are appointed. While it might be a colorable argument that a referendum isn't "legislative," there's no antagonism between the state legislature and the referendum process. Legislators often place initiatives on the ballot themselves, and are often constitutionally required to do so. So, it'd take an unusually harsh reading of the text to consider this method wholly inconsistent with the Constitutional requirement of legislative direction - basically a ruling that the California state constitution has an unconstitutional division of powers.

Second, the federal courts have a lot of procedural firewalls to save themselves from even touching contentious issues like this one. There's no pay-off for them in rendering a decision, and no imminent threat to the Constitutional system in getting involved. The federal courts can toss a case out of court on the basis that the parties don't have "standing" to litigate the issue. It's unlikely the Court would find any likely plaintiff to have been sufficiently harmed or possess significant enough interests to raise the issue in court. They used a similar dodge to avoid deciding if Bush and Cheney were both Texans, thus creating a Constitutionally impermissible result of President and Vice President both coming from the state.

Third, there are other provisions of the Constitution which support granting wide deference to the states in figuring these things out on their own... Courts have held since the nineteenth century case of Luther v. Borden that the "Gurantee Clause" which guarantees a "Republican form of government" for the states can't be enforced judicially (Rhode Island was basically in a civil war, with two rival governments asserting legitimacy - the Court refused to choose between them). The Tenth Amendment's reservation of powers to the states would also pull the justices strongly towards ruling that the issue either couldn't be litigated (sovereign immunity) or that such decisions are entirely up to the state."

I don't know if this counts as a double post, but no one really read it the first time. I would have linked to the post but it is only a short section of a longer thread. I am inclined to agree with Geoff. The courts may just side-step the issue.

If the case is taken, I think that there is plenty of leeway provided by various precedents (pointed out by previous posts, notably chris123987 and login1wfp) for a judge to decide either direction on this issue.

This argument is probably moot as it is very unlikely that the initiative will pass, but I will enjoy my turn as a de facto member of the CA legislature.