So, I have been looking at the Constitutionality of the Executive Order and what the Constitutional law folks are saying. The short answer is that, on its face, the travel ban is Constitutional and within the President delegated authority. However, the manner in which it is applied may be a violation of Constitutional due process / equal protection. As I understand it, it was on this basis that the federal district court granted a temporary stay.
This is a Presidential Order that is administering executive authority delegated him by Congress pursuant to federal immigration law. Further, the Executive Order covers only those countries specifically identified by Congress and the Obama administration as “countries of concern” that have been determined to have a "significant presence" of a foreign terrorist organization or to be a safe havens for terrorists.
Under current federal immigration law, the President has broad authority to prohibit people from entering the US:
8 U.S. Code § 1182 - Inadmissible aliens …
(f) Suspension of entry or imposition of restrictions by President
Whenever the President finds that the entry of any aliens or of any class of aliens into the United States would be detrimental to the interests of the United States, he may by proclamation, and for such period as he shall deem necessary, suspend the entry of all aliens or any class of aliens as immigrants or nonimmigrants, or impose on the entry of aliens any restrictions he may deem to be appropriate.
In addition, the countries to which the ban is applicable were specifically chosen based on prior Congressional and Executive action. The seven identified countries are from the list covered by "Visa Waiver Program Improvement and Terrorist Travel Prevention Act of 2015" initially identified by Congress and, subsequently, supplemented by the Obama administration. The Bill was a bipartisan act that was signed into law by Obama in December 2015. It was passed overwhelmingly by Congress (407 – 19). Initially the law barred individuals “from Iraq, Syria, Iran and the Sudan, or those who have visited those countries in the last five years, from traveling to the United States without a visa.” In February 2016, , the Obama administration identified Libya, Somalia, and Yemen as “Countries of Concern” under the act and barred individuals from these countries as well from travelling to the US without a visa.
http://www.cnn.com/.../visa-waiver-p...use/index.html
https://www.govtrack.us/congress/bills/114/hr158/text
https://www.dhs.gov/.../dhs-announces-further-travel...
In challenging the Order, it is almost unquestionably Constitutional as written but the Constitutionality of its actual application is much debated. Given that (1) the vast number of Muslim dominated countries are NOT on the list (including the largest – Indonesia); and (2) on its face, it is limited to "countries of concern" as identified by Obama’s Dept. of Homeland Security, I would suggest that the Order is facially Constitutional because it is specifically related to national security and not, strictly speaking, a “Muslim ban.”
Rather, the attacks on it that were – temporarily – successful attacked the actual application of the Order – deprivation of a property right without due process and deprivation of equal protection under the law. However, this due process/equal protection aspect can be remedied going forward since notice of the intended deprivation has, in fact, been given and all that need be implemented is a process to contest any individual ban. This does not require a full blown hearing/trial but need only allow the individual to be heard before a neutral decision maker.