And Obama can't unilaterally change the Constitution, either, but there is no need to do so when ignoring the law accomplishes the same goal.
Obama can’t rewrite the Constitution, but he can pretend it doesn’t exist, or it says whatever he claims it says, and you and I are compelled by the power of the state to act as if the Constitution says whatever Obama says it says. The power of the Catholic church is moral suasion. If the pope proclaims that gay sex is permitted, every priest that performs a gay marriage is still going straight to Hell (with all the standard caveats about the possibility of conversion, the requirement for action under free will, etc.). Further, he adds to his torment the punishment of every soul who he misleads into gay marriage. Further, the bishops bear at the cost of their own salvation the burden of doing everything possible to declare him a heretic and an anti-pope and refuse his teaching.
In a way, I think that this pope is imprudent, yet not heretical may be a blessing. For too long, conservatives have simply responded to heresy by saying, “the pope says...” The confusing, ambiguous language of this pope is making orthodox stand up for doctrine, not merely a cult of personality.
And that is no criticism of John Paul II or Benedict XVI! They needed a little bit of cult of personality to counter the insane liberalism of the Post-Vatican Council, and the Holy Spirit blessed them with it! But now that orthodoxy is better re-established, I believe the Holy Spirit is training orthodox Catholics to stand on doctrine, not a mere appeal to authority.