Yes, Congress can simply pass a law (once a good conservative such as Ted Cruz has been sworn in). That is IF the despicable Mitch McConnell allows it to pass the Senate. He has a million excuses for why he can’t pass laws that are for the good of the country ...other than those good for the ‘RATS or the GOPe campaign contributors and lobbyists.
I don’t think Congress has to pass a law because as the Breibart article explains, based on a reasonable argument applying the Constitutional as written and originally intended and understood along with well-reasoned case law, denying citizenship to the children of illegal aliens is fully consistent with the Constitutions Fourteenth Amendment.