The Orthodox would love to be in union with Rome. In fact, Fr. Thomas Hopko gave a short list of requirements in order for union to become a reality: http://www.orthodoxytoday.org/articles6/HopkoPope.php 

The first requirement is that the Pope "would have to confirm the original text of the Nicene-Constantinopolitan Symbol of Faith and defend its use in all the churches, beginning with his own. At the very least (should some churches for pastoral reasons be permitted to keep the filioque in their creed), he would insist on an explanation that would clearly teach that the Holy Spirit "proceeds from the Son" only in relation to God's saving dispensation in the world. He would make certain that no Christian be tempted to believe that the Holy Spirit essentially proceeds from the Father and the Son together, and certainly not "from both as from one (ab utroque sicut ab uno.)." "