This is part of the welfare objection. Below is a quote from Mark Krikorian’s book, where he makes the case specifically in the context of immigration to the United States.
The role of immigration in increasing the cost of education is especially large because immigrant women are more likely to be in their child-bearing years, and immigrants generally have larger families. So while immigrants constitute about 12 percent of our total population, the children of immigrants (some born here, some immigrants themselves) comprise 19 percent of the school-age population (five to seventeen years old) and 21 percent of the preschool population (four and below).36 In California, nearly half the children in both age groups are from immigrant families. While more than two thirds of these children are native born, their use of American public schools is a direct result of our immigration policy allowing their parents to enter. Total school enrollment nationwide reached a post-Baby Boom low of 44.9 million in 1984, and is now at about 55 million.37 This means that the 10.3 million school-age children in immigrant families account for all—100 percent—of the growth in elementary and secondary school enrollment nationwide over the past generation. Obviously this isn’t the case in every school or every town or even every state. But in the nation as a whole, the surge in school enrollments is due entirely to the federal government’s immigration policies. This immigration-driven growth in enrollment has caused overcrowding at many schools. The U.S. Department of Education has found that 22 percent of public schools are overcrowded, with 8 percent of the total being overcrowded by more than 25 percent of capacity. The overcrowding is worst in precisely the kind of schools immigrant children are likely to attend: large-capacity schools in central cities, especially in the West, especially those with more than 50 percent minority enrollment, where the majority of students receive free or reduced-price school lunches (i.e., are from poor families).38 The education expenses incurred by this immigration-driven surge in enrollment are huge. One study, which looked at only part of the impact of immigration, found that education of illegal-alien students cost the states $12 billion a year, and when U.S.-born children of illegal aliens are added, the cost more than doubles to $28.6 billion.39 California was estimated to have spent $7.7 billion on education for the children of illegal aliens, nearly 13 percent of the state’s total education budget for 2004-2005. And this cost estimate did not take into account the extra expense of educating immigrant students as opposed to native-born students; a study conducted some twenty-five years ago found that even then, bilingual education programs cost from $100 to $500 more per pupil, while a more recent look at California found that supplementary programs for “limited English proficient” students cost an extra $361 per student.40 Another more recent study, of Florida, found that “ESOL [English for speakers of other languages] students cost $153 million in fiscal year 2003-04 beyond what they would have if enrolled in basic programs.” 41 Across the nation, this adds up, since about 10 percent of all public-school students are considered limited English proficient, otherwise known as “English language learners.”42
Krikorian, Mark (2008-07-03). The New Case Against Immigration: Both Legal and Illegal (pp. 175-176). Penguin Group. Kindle Edition.