Yes. The Pope could direct the President of Notre Dame to recind the invitation but don’t look for it to happen soon, if at all. The idea that this president of the United States is headed to Notre Dame is a teaching moment for millions of Catholics and serves to highlight the moral decisions this president has made.
I wouldn’t be surprised that as this heats up, a way out is sought.
No, the pope CANNOT do this. Ex corde ecclesiae makes this clear—and it was a papal document. Catholic universities have autonomy in making these sorts of decisions. They are supposed to make them in accord with Catholic faith. But the remedies available to the pope (and to the local bishop) do not include authority directly to reach in and tell the university that it cannot honor Obama.
What the pope and bishop can do is say, “if you do go ahead and honor him with a degree, I will canonically deny you the right to describe yourself as a Catholic university.” The pope will not reach in and interfere with the local bishop on this, however.
Stop looking to the pope to solve everything. Subsidiarity says that the point man here is the bishop. But he has less direct control over Notre Dame than do parents, alumni, students, faculty, trustees and donors. They, in law, have more power than the bishop does, except his power to threaten the university with denial of the label.