I do not disagree that immigration should be easier, especially when those immigrants are fleeing famine and/or war, but immigrants are always stepping into a "political equation" and the politicians with power
(not always the elected politicians) are determining who will get the money, which is how they balance the "political equation". If the current "political equation" involves "hardships at home, people will need to tighten their belts, etc", then bringing in migrants will not fit in their equation, so those politicians will find a reason to reject most of the refugees, even if they would provide more valuable labor than the cost to feed and shelter them. This
article about rejected european jewish refugees during WWII includes a US diplomat's suggestion that France fell fast to Germany because France accepted a wave of Jewish refugees (search the article for "William Bullitt" to read this lovely quote, which can also be found in USA congressional records). Every potential immigrant to America is met at the door by a politician and his "business" friends who are asking, "what are you going to do for us? Want to be my economic slave?" The Irish fleeing the Potato Famine and the Italians fleeing the unification in Italy, entered America and went through this until they gained their own political power.