Democrats oppose adding this question to the census because they suspect, with good reason, that non-citizens, especially illegal alien non-citizens, will simply refuse to be counted in the census rather than reveal their citizenship status.
This may also be a problem for legal immigrants, those in the United States on a visa or green card, because people do overstay their visas; a large percentage of the illegal population in America came in legally and has simply overstayed their visa. So the fear of Democratic and liberal groups is probably very well founded; certain few illegal persons are going to want to admit it on a census form and many legal immigrants may skip the census as well.
If millions of non-citizens refuse to participate in the US Census, the Democrats will take massive political beating. That’s because electoral districts must be drawn based on population. The non-citizen population resides in heavily Democratic areas; if they are not counted, those areas will not have sufficient population to support Democratic congressional and legislative districts, especially in the big cities. Democrats could lose dozens of districts just due to too few people being counted.
Early in our history the census began asking a whether the individual being enumerated was born in the United States. After the Civil War, with the huge boom in European migration, the census asked whether the person was a citizen eligible to vote. Beginning in 1880, the census asked the place of birth not only of the enumerated person but of the parents as well.
With the 1890 census the question was asked: are you a naturalized citizen or not. The year of immigration of a foreign born person as well as the year of naturalization (if naturalized) was asked in the 1900, 1910, 1920, 1930, 1940 and 1950 censuses, in other words for the first half of the 20th Century.
However, in 1960 the question was dropped and the Census Bureau explained why: the great migration had long since ended; very few non-citizens lived in the United States so the question was no longer relevant.