Still had what chance? They never had a chance. Roosevelt wasn’t opening the doors to allow European Jews to move to America. There were strict immigration quotas. And those quotas were all filled, so it wasn’t like more immigrants were welcome to America.
Besides that at the time living in America was a spiritual danger. (Throwing tefilin in the Hudson, working on Shabbos, etc.) And better to live in a place with a physical danger to your life than to live in a place with a spiritual danger to your neshomo.