The two objections I have seen most often in commentary are that Trump's order fell afoul of the 1965 Hart-Celler Act (https://www.nytimes.com/2017/01/27/opinion/trumps-immigratio...), or Trump's EO fell afoul of 8 U.S. Code § 1152 (https://www.law.cornell.edu/uscode/text/8/1152).

I have seen a lot of commentary arguing one way or another regarding this issue. My personal conclusion at this time is "firmly grounded" would be too strong of a statement, in my opinion.