No, it's not a leap it's a core prescription of Christian practice. The Parable of the Good Samaritan illustrates this. You are to treat your neighbours well, and your neighbours are anyone in need of your mercy.
Does that include letting them live in our country illegally while they live off of welfare payments?
Probably, yeah. Jesus was a radical and the USA is rich. But with that being said, I'm not the one advocating for a Christian nation.
Oh, is that all he said about how you should treat others? You're right, he'd probably advocate for strong territorial integrity and not at all be concerned with poverty and hunger. Jesus was the first libertarian after all.