I have consistently heard rumors that the Orthodox and the Roman Catholics will be reconciling at some point (at least to the point of Catholics being able to receive Orthodox sacraments). Sometimes the rumors are that it will happen during a reigning patriarch, but other voices among the Orthodox have suggested that such a gesture is an impossibility*. So, which is it? Is reconciliation possible (and close), or will things continue as they have for nearly a millennium?
As to the differences from a Catholic man's perspective:
So, is it likely that these two Churches will reunite? It is the hope and prayer of every Catholic person that they will. It should be the hope and prayer of every Christian that 'all [Christians] may be one', such as The Father, The Son, and The Holy Spirit are. At the same time, both of these Churches do believe that a union without a consensus on the deep issues that divide them is artificial, and not a real union at all. Thus, they both believe that they need to work on these fundamental issues beforehand.
And herein lies one of the problems. For, while the Pope can speak for all Catholic Bishops, ratifying their declarations, there is no one in the Orthodox Church that can similarly speak for everyone. If, and when, reunification takes place, there will always be a substantial amount of Orthodox Bishops which will renounce the reunion as heretical and will refuse to reunite.
Another problem: there are some teachings that the Catholic Church deems as irrefutable, due to the dogma of infallibility. To go back on these teachings would amount to a declaration that the Catholic Church is not infallible, which I fear She cannot do. The best The Catholic Church can do is to recast (re-explain) those same infallible teachings on a new light, perhaps making it logically possible to come to a formulation of the teaching which is also acceptable to the Orthodox Church. Given that both Churches have very gifted and careful theologians who feel themselves in the right, it is very difficult to see how this might be possible.
THEREFORE, what are the chances that both Churches would unite? Very unlikely, if you ask me. History may force them to reunite (and force them to work out those differences), if a world-wide effective persecution of both Churches should occur, but other than that, all we can do is hope and pray.
The Catholic understanding is that the lack of reconciliation is due to a lack of love when Catholic and Orthodox share in full all doctrines that would make full communion appropriate.
The Orthodox position is that there is much more than the clause in the Creed and Catholics are saying, in effect, "Let us restore communion despite our unresolved differences."
It is my own experience that Catholics who seek reconciliation never seek to resolve the unreconciled differences or otherwise acknowledge what they have to repent of for any appropriate reconciliation to be possible. The Orthodox experience here is kind of like the Catholic experience when Anglicans or Baptists want to share the chalice without changing any of their doctrines.
(See my own Open Letter to Catholics on Orthodoxy and Ecumenism.)