I look in vain in the Constitution for where the president has unilateral authority to ban people from entering the country based on nationality and/or religion.
It's not based on nationality or religion, dummy.
It's based on national security. And yes, he not only has the authority, he has the duty.
So he's specifically making the case based on the country people are coming from and their religion, but that has nothing to do with nationality or religion? Find for me in Article 2 of the U.S. Constitution where the President is given authority to ban people from entering the country all on his own.
I do enjoy seeing conservatives suddenly completely uninterested in what the Constitution says all of a sudden. Very amusing.