Desperation to change the rules on immigration even though Congress wouldn’t act is what made Obama rewrite the immigration laws on his own. Trump should resist the same temptation.
Regardless, if the president goes down this route, he will likely get swamped in the courts. There would be an immediate injunction. A case might not even make it to the Supreme Court, and the courts wouldn’t even have to speak to the underlying issue of birthright citizenship—they could just rule that the executive order exceeds the president’s authority.
Even such a limited decision would be widely interpreted as an affirmation of the current interpretation of the 14th Amendment, setting back the cause of changing birthright citizenship, rather than advancing it.