a person cannot "be illegal". they can perform acts which are illegal, sure, but to call them "illegals" is just dehumanizing rhetoric that adds absolutely nothing to the discussion.
Does US have such a lack of space to fail to absorb 2-5% increase over years?
What's so hard about naturalizing or legalizing them, so that they can more easily interact with current power structures on the territory?
Capital city in the country where I live got a 25% population bump over a few months a few years back, of people who didn't even speak the language. Barely anything appretiably negative overall happened.