I feel that this is an area that American Christians have had an ironically hard time in accepting. Frequently, I see people who claim to be Christian also support the closing of borders to immigrants. Sometimes, they even use references to the "gates of heaven" when doing so. Even though in nearly all cases, they are the descendants of immigrants, they fight against allowing others to reap the same benefits that they have enjoyed.
For me, the most Christian aspect about America is its acceptance of all people. In fact, quite often the early immigrants were the cast-offs of humanity--exactly the type of people whom Jesus raised above all others. The open welcome of Christianity to all people is a core tenant of our faith. Would that Christians themselves be more open and welcoming to others--especially the poor and downtrodden.