The most obvious one is that the modern welfare state relies for its legitimacy on social cohesion, i.e. a certain base of shared values and identity. You will not get people to consent to heavy taxation and redistribution if they feel that their society is full of foreigners. This observation is perhaps more relevant to Europe than the USA.
And that's before mentioning the economics of funding a welfare state with a relatively static/shrinking tax base and growing, imported, welfare recipient class - the latter being practically unbounded in the case of illegal immigration.
