Many experts think the case would be close because the president does have a lot of leeway in immigration. But if a policy is seen as having a religious test, that could run afoul of the First Amendment in the eyes of the justices. In the campaign, Trump openly called for keeping Muslim visitors out of the country. As president, his executive action is not explicitly against Muslims but would apply to people coming from six countries with mainly Muslim populations.
US District judges Watson & Chuang even stated that Trump's campaign rhetoric of banning Muslim were used as grounds to halt the ban.
"Donald J Trump is calling for a total and complete shutdown of Muslims entering the United States."  I guess like "wire tap" should not be taken literally, this statement shouldn't be taken literally either.  Just like "Mexico will pay for the wall?"  Dummies!!!