Ummm ... the relevant portion of the 14th amendment states “Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, EXCLUDING INDIANS NOT TAXED.” (capitalization mine)
Many illegal aliens are, in fact, Indians not taxed. Lest you dispute that they are Indians, I refer you to the common claim made by many Hispanics that “we didn’t cross the border, the border crossed us.” In other words, THEY believe they are Native American (as, in fact, they generally are). The numbers of Native American persons who are not taxed (i.e. the vast majority of illegal aliens) is specifically excluded from being used for apportionment of representatives. The language could not be more clear on this point.
Three things wrong with that argument: (1) "Indians not taxed" was an 18th & 19th century legal term meaning Native American tribes that were still functioning as independent sovereign nations and had not yet been conquered by the U.S. It has no application today.
(2) Many illegal aliens are not "Indians" in any sense of the word-- should the census count the illegal African immigrants in New York but not the illegal Mexicans in Texas? Or count the illegal Haitians in Florida but not the illegal Dominicans living next door to them? What sense would that make?
(3) Unlike the independent Indian tribes of the 1870s, all illegal aliens are certainly "taxed" to some degree or other-- if nothing else, they pay sales taxes and federal gasoline taxes. Many also pay federal income tax because they are working with forged Social Security cards.