This assumes that the other countries will comply with the administrations requests for information on the individuals, otherwise it will be extended indefinitely. Iran doesn't have a US embassy and they don't officially have relations with the US, you think they're going to suddenly start handing over information to the US? If anything, this gives them more reason to say, "See how the US is treating us like shit?" which further stirs up anti-US sentiment among them.
Also, yes, green card holders ARE affected by this. My wife won't be able to leave the country without fear of being denied entry upon her return despite her being a valid green card holder.