The world is not the responsibility of the United States. Anyone who is allowed to come to this country as a legal immigrant is granted a privilege of great value, but it is not a right than can be demanded by anyone.
If indeed we are responsible for the entire world, we should simply impose our form of government, language, and culture upon the rest of the world, instead of forcing these poor refugees to traverse long distances under harrowing conditions. If being part of the United States is the ultimate good one can do for “the poorest and most marginalized”, then it stands to reason that we should do our best to expand the scope of our dominion, so that people don’t have to move. We could impose a diversity of thought and culture across Iraq, Syria, Iran, Sudan, Libya, Somalia and Yemen, forcing them to allow women to have equal rights under the law, forcing them to allow homosexuals to live without the threat of the death penalty, forcing them to abide by the separation of church and state by eliminating sharia law.
Or, we could accept that those seven nations must find their own path out of barbarism, that we cannot blindly allow people from those countries to come to the United States without extreme vetting, and that it may be more cost effective to create safe zones in those various regions to server a greater number of refugees.