I don't know how much impact, in functional terms, of implementing such reform in the US would actually be. Legally, in most jurisdictions, emergency treatment is required to be provided to ill persons, regardless of citizenship, thats a public goods failure in the event that such service is provided to a non-citizen. Any cost to the citizenry in this form would not be negated by such reform.
Similarly, statistics bear out that the more costly social programs are not taken advantage/opportunity of by the first generations of immigrants, the rate rather increases with the number of generations one is removed from immigration. Inductively then, this would not really be as significant a concern.
The necessity for such legislative action in NZ may come from the fact that public expendature to beneift citizens exceedes that of the US on a per capita basis.
Further, much policy aimed at benefting the citizenry of the US is codified in the incentive structures inhernet to business and other tax codes (writeoffs for employer and employee spending on retirement funds, healthcare, insurence and other such programs that have a positive impact upon the average standard of living).
The vocations of individuals who would not be considered citizens, were such legislation implemented in the states, are rarely connected to such things as retirement funds, healthcare and insurence. As there is an inherent trade-off between the provision of tax incentives and the revenue that the governement could collect in the absence of the incentivising tax breaks, in the event that these incentives are not often taken advantage of by the employers of the abovementioned individuals there would be no taxable expendatures that could be factored into the equation, making the 'cost' less.
There is also an efficiency argument to be made with regard to the availability of inexpensive labor in the form of immigrants and the successive generations which are not far removed from immigration themselves.
One significant question remains: What would happen to the status of the children of an individual if that individual were to gain citizenship after having resided in a country for a term of time, their children having been born there and not afforded citizenship as a function of the regulations in place?
Quite frankly, I personally could care less weather or not such reform is implemented in the US, just thought I'd get into the structural implications a little bit as argumentation based in economic issues is always soon to follow from immigration/naturalization-based discourse.
sorry to ramble on.