It looks like the answer might be yes. At SCOTUSblog, Lyle Denniston has a quick analysis of this morning's oral arguments in the campaign finance case Citizens United v. FEC:
Three Justices—Anthony M. Kennedy, Antonin Scalia and Clarence Thomas—have explicitly urged the Court to overturn the two precedents that sustained congressional limits on campaign financing by corporations and labor unions. Kennedy and Thomas only seemed to reinforce that position on Wednesday; Thomas remained silent, but had given no indication earlier of a change of mind.
That lineup has always put the focus, as the Court volunteered to take on new constitutional questions in the Citizens United case, on the Chief Justice and Justice Alito. While both have been skeptical in the past about campaign finance laws, supporters of such laws had fashioned an array of arguments they hoped would lead Roberts and Alito to shy away from casting their votes to create a majority to free corporations to spend their own treasury money to influence federal elections. None of those arguments seemed to appeal to either Roberts or Alito.