I don't think that ending birthright citizenship in the US would be a big deal. Outside of the Americas, birthright citizenship isn't really a thing. I'm sure the world would adjust if the US decided to close this path to citizenship.
However - it is part of the Constitution, and if _this_ Supreme Court isn't prepared to tear it up, nobody will. Nor can Trump simply avoid a "long and unwieldy Constitutional Amendment" - Congress can't unilaterally override the Constitution. That's the whole point.
(What he _might_ be able to do is declare non-citizens - especially ones without visas - not subject to US laws. Basically giving every undocumented migrant diplomatic immunity. That would prevent birthright citizenship if _both_ parents are undocumented - but that's a pretty big change)