I’m always glad when people refer (in an unironic or unmeta fashion) to the Statue of Liberty and/or the poem “The New Collosus” by Emma Lazarus when writing about immigration. It serves as a big flashing neon sign that the person in question has nothing useful or insightful to say.
The building of the Statue of Liberty had nothing remotely to do with immigration and the poem, forgotten for years, wasn’t even added until after Lazarus’s death after a campaign by well-meaning friends. Anyone who doesn’t realize it is not actually law, but just a decoration on a statue that is primarily about something else is too uninformed to take seriously.
The poem itself is mixed, it has about two good lines and the rest is dreadful, sentimental doggerel. It should no more form the basis (or be any part of) debate on reasonable immigration policy than the song “White Christmas” should be the basis (or part of) the debate on Climate Change. Trying to use it as an argument is an admission of having no good arguments.