I would carve out the North Eastern United States (Mid Atlantic, Great Lakes, New England) along with the Eastern provinces of Canada if they wanted to join.
I would call this ... Atlantica.
We would be known for a sizeable economy along with relative social diversity and tolerance. We would combine a president and a multi-party democracy like they do in France. There would be relatively limited government in both economic and personal spheres, and a complete separation of church and state.
All Atlantica troops overseas would be withdrawn. Instead we would beef up internal law enforcement and intelligence to deal with any terrorist threats. Since there wouldn't be any Atlantica troops within 5000 miles of Mecca, perhaps terrorism wouldn't be a major concern to begin with.
We would strengthen trading and political ties with Western Europe, as the "establishment " in Atlantica is noted for being old money with close ties and heritage to Europe. We would try to institute a North Atlantic Free Trade Agreement to replace the now defunct North American Free Trade Agree ment.
What happens to the rest of North America is open to question. I suspect that the West and the South would separate to form Pacifica and Dixie, respectively. We would maintain trading relations with Pacifica and Dixie if it suited our purposes. However, given the cultural and political differences that Atlantica has with Pacifica and Dixie, it is doubtful that a political reunion would ever be tempted again. If we looked for allies, it would be with Europe, specifically Britain.