I am not sure why you are fixated on this question, first of all it is a straw man argument since you are asking a politically charged question in a thread about christianity, second you already know the answer (he would welcome all who want to come to Him), and third i do not believe He would be at the border since that is not a ripe stomping ground for transformation in life. Jesus was all about changing personal lives, He never turnwd anyone away that truly wanted to be transformed, but he did turn away people who only wanted the superficial changes or didnt want to change at all.
Make no mitake about history, Jesus lived in a time when there was great political turmoil, our time has no claim to being the most politically tumultuous time ever, yet we hear Jesus soeak very little to the political world, and only when directly asked by the rulers of his area during his trial. His message was about the eternal not aboyt the wordly.
So to really soeak about your question, we would have to ask ourselves what tue immigrants are coming for. Are they coming for a better earthly life? Or are they coming searching for eternal life? Because Jesus was interested in the latter and wanted nothing to do with the former. I am sure there were plenty of people in His time that struggled in their day to day survival and He had not much to say about them.
Does that answer your question?