While these concerns have a natural constituency in the White population they aren't confined to it. As has been noted on this thread many Blacks and Hispanics are also concerned about immigration. I mentioned the White minority question because it comes up often, but Blacks are very much aware that immigration dilutes their stake and status in the country, and many Hispanics are also disturbed by the effects of high immigration, as some of the posts on earlier threads about this topic indicate.
Representative government means responsiveness to the concerns of the public. Lyndon Johnson's stroke of evil genius was to convince the ruling class that the wishes of the majority could be characterized as those of a race, therefore as racist and therefore unworthy of consideration, thereby allowing the government to disregard the wishes of the majority of Americans, whatever race they may be. A government that is more responsive to the wishes of those who want to come here than to those who are already here isn't working in the interests of its primary constituency.