No, actually they cannot. Since the Supreme Court has "made new law" in this area, it cannot be overturned by "mere voters". A large majority of voters are in favor of the "open primary"---but the Dem and 'Pubbie power stucture aren't.
For the very good reason that the Republican nominee in an election should be someone supported by Republicans, not someone supported by a few liberal Republicans, a bunch of independents, and some Democrats who crossed over. Not many here would be happy if an open primary gave McCain or Giuliani the Republican nomination. Even worse are the elections where people cross over to intentionally support the weaker candidate in the opposing party's primary.