This CalBuzz article says Democrats in the California legislature may introduce a bill (or amend another election law bill to add a new provision) soon to provide that initiatives, no matter when they are submitted, will not appear on the June primary ballot. Instead they would wait and be placed on the November ballot. The rationale is that initiatives should be on the ballot that draws all voters to the polls. Democrats believe that the June 2012 primary ballot in California will have low turnout from Democrats, but high turnout from Republicans, because the Republican presidential primary will theoretically be exciting but the Democratic presidential primary will not be exciting. Therefore, the voters who show up in June would be skewed.
The June 2012 primary will also contain U.S. Senate, U.S. House, and legislature, but again, in 2012, the U.S. Senate race is likely to be more exciting for Republican voters than for Democratic voters, because incumbent U.S. Senator Diane Feinstein is running for re-election and no Democrat with any support is expected to enter the race against her.
California currently is the only state, or almost the only state, that ever permits statewide initiatives to appear on a primary ballot.