How does O'Sullivan describe the future realm of the U.S.?
John L. O'Sullivan is largely credited with coining the term "Manifest Destiny.O'Sullivan, editor of The Democratic Review and ardent supporter of the Democratic Party supported the annexation of Oregon and Texas territory in an article in which he stated:
Our manifest destiny is to overspread the continent allotted by Providence for the free development of our yearly multiplying millions.
In a second article, published on December 27, 1845, he wrote:
And that claim is by the right of our manifest destiny to overspread and to possess the whole of the continent which Providence has given us for the development of the great experiment of liberty and federated self-government entrusted to us.
To O'Sullivan, God had given the whole of North America to the American people as something of a "promised land," in return for which they were responsible for spreading Republican style democracy. O'Sullivan saw the destiny of the United States as something of a moral, or "higher law;" so much so that it transcended International Law. Even so, O'Sullivan did not support military intervention. He believed that since this was the manifest destiny of the people of the United States, it would happen inevitably with the immigration of Anglo-Saxon Americans to other areas--the culture would follow the people. Interestingly, he opposed the Mexican War, although he later stated that the result was beneficial to both the U.S. and Mexico.
I assume that you are referring to John L. O'Sullivan's article "The Great Nation of Futurity." There, O'Sullivan describes what he sees as the destiny of the United States. In the article, O'Sullivan's vision is that America will create on Earth the most perfect society possible. He argues that it will
... establish on earth the noblest temple ever dedicated to the worship of the Most High -- the Sacred and the True.
To O'Sullivan, this would involved territorial expansion. He said that the floor of the US's "temple" would be a hemisphere and the roof would be the sky. But this is not the main point he is trying to make. What he is saying is that the future United States will be a place that is holy, one whose ways are based on the dictates of God.
O'Sullivan, then, believes the future US will bring God's will to earth by establishing freedom and liberty in its (expanding) territory.