A Common Gaze

I'm old enough to remember the revolutionary "Ecumenical Movement" of the 60's. I applaud all those who broke through the status quo to extend the hand of fellowship to people who didn't worship in the same building with them on a Sunday morning.
I remember my mother taking us to the Congregational Church, just down the street from our Roman Catholic parish. I was a little nervous, never having been in anything but Catholic churches. But I remember that night, it felt special, like Christmas. It felt holy, and important. Could my eight year old little heart have sensed the Father's pleasure over His children coming together?
It was an attempt. I've heard criticisms of the movement over the years. It wasn't perfect, but I believe it was born out of something in God's heart. Imperfect though it may have been, it was an attempt.
I don't present any answers here. Just a question: what would happen if, for just one month, or one week, all across the globe, the people who love and believe Jesus is the Son of God, that He died and rose and is coming again, what if for one week, we didn't focus on our differences. I'm not saying we let go of our traditions, or doctrines. But what if we entered into a short time of a common gaze, a lifting our eyes as the chosen race that we are?
What would the impact of all of us experiencing His intentional loving gaze at the same time do to this old, still dark world?