Emma Lazarus wrote poetry, not policy. And that was back in the late 19th century, when America was still largely wilderness and there was no wlefare state, islamic terrorism, or MS13. Besides, Liberty welcomes all LEGAL immigrants, not every creature who can stagger to our border.
But why am I wasting my time responding to the maudlin ramblings of a fake priest?
If my memory serves me correct, that poem was placed at the Statue about twenty years afterward. The Statue originally had nothing to do with immigration, but liberty.