Simple thinking logically, the average American, whether born to citizens or not, does not pay enough in taxes over their lifetime to balance out the services they use. If they did, we wouldn't have an $18T and growing debt. Given that, the faster our population grows, the faster our deficit spending grows.
If our spending was under control, I'd agree with you. But it's not. So every new American is a burden rather than a benefit.
If every new American is a burden then logic says the optimal outcome is a shrinking population. I can't say I know of many economists that would agree.
Remember also that our debt is overwhelmingly owed to ourselves. More importantly, the question is if a person raises or lowers our debt/GDP ratio, not whether they increase our debt in the absolute. For example if someone adds 1% to our GDP and 0.5% of GDP to our debt, they have made America's debt situation better, not worse.
