Whenever a Democrat says that some part of the economy depends on illegal immigrants, they are usually compared to slaveowners who insisted that the economy relied on slavery. This talking point rarely makes sense in the context of the broader immigration debate.
Democrats are also accused (not without basis) of wanting to give free healthcare to illegal immigrants, wanting illegal immigrants to vote, caring more about illegal immigrants than native-born citizens, and wanting to offer full citizenship to illegal immigrants. So if the Democrats think that illegal immigrants should be treated like slaves, they're doing a bad job of it beyond the vaguely similar talking point of the economy depending on a particular group of people. How is the side that wants more rights for illegal immigrants across the board the side that wants to enslave them?
There was also a time when people wanted to ban Chinese laborers from the workforce or even black workers from machine work, so if the whole debate is about who can be compared to racists in the past, there's plenty of ammunition for Democrats to use.
And besides, is bringing up the economic impacts of immigration not warranted if Republicans bring it up too? If a Republican says "illegal immigrants will take our jobs and destroy the economy," that seems like it's inviting someone else to bring up positive economic impacts of illegal immigration, whatever those may be. If a Republican says "we don't owe these illegals anything," then shouldn't they want the illegal immigrants to be a servant class? It seems like Republicans solely care about the effect of immigration on natives until Democrats start talking about the effect of immigration on natives, then Democrats are suddenly racists who don't care enough about illegal immigrants (despite wanting illegal immigrants to have more rights).