Many restrictionists argue that the high numbers we experience now are so high that we will not be able to adequately assimilate and integrate them into American society, thus setting the stage for inter-group strife and the degradation of civil society.
I tend to think they state the problem the wrong way around. It is rather the strength of our assimilation policy that determines how many immigrants we can welcome. Certainly America welcomed a higher percentage of foreign-born during the height of the immigrant boom in the years before World War I, and successfully assimilated them. This should be an existence proof that we can, given the right circumstances, do the job again.
However, this does not mean that the economic reductionists who make every social issue a matter of employment figures and economic benefits can assume that assimilation will be automatic. A closer look at the experience of 1890-1920 shows that America experienced many of the problems with immigration that we do again today: public health challenges, concerns about integration into civil society and the sharing of democratic discourse and values with people who had no previous exposure to such things, and rising levels of crime and corruption in high immigration areas.
As a response to these challenges, many reformers and activists of that era expended much effort on integrating immigrant groups, fighting the crime, poverty, and corruption that came with them, and in promoting an assimilationist agenda. This effort was in the end successful, culminating perhaps in the successes of World Wars I and II, where Americans of every immigrant group, including nationals of the states with which America was at war, gave a high degree of support to the war effort, and receiving in return a genuine acceptance from the general population.
The point is, and this is a point now usually ignored, that it was neither automatic nor effortless to assimilate these people.
Unfortunately, multi-culti pieties make it hard to even talk about these issues.