Mary
We decide if the person is here legally or not. We could choose to allow crossing the border to work as a legal action. Similarly we could allow those who chose to work under those conditions to pay a 10% non citizen tax and charge a 5% matching employer tax. We do not have to make them citizens, add them to Medicaid, or social security. We actually need their children more than we need the parent. As the US birth rate is fewer than 2%(1.4% and dropping). We have a smaller percentage of babies/young people than needed for a population our size. See we can only have about 19% in k-12 schools, yet we need >25% in these schools. As you mention the babies are of our culture not a foreign culture. These babies will be important when you and I need nurses, doctor, mechanic, etc, etc, there simply would not be enough young US citizens to perform the functions. That would mean in our old age we could not afford these services. So we need them to pay the taxes and provide cheaper services.
The fewer people would simply raise their prices to ration their services, which is the way free markets work… Japan already suffered this fate you may want look at their 1990’s economic problem. Just think if we close the borders then issue our old people $24k in SS checks + $12k in Medicaid, then give them a income tax bill for $4k. We will need to increase sales, state, and other taxes. These old people will live in poverty, on rationed services. However the young which will live in the depressed economy may do well, as their services are auctioned to the highest bidder. And there will be abundance of old peoples assets (houses, land, jewelry, etc). The old people living in poverty will be in a constant sell off mode. I simply can not see why you wish to do this to our old people?