There's no question that the POTUS has broad constitutional authority to ensure the safety of the USA and its citizens. However it's completely unjustified for the Trump spokesperson to say that the judiciary can't rule on that order. In fact, it's precisely their job to rule on it if the order is challenged.

The reason why the order was challenged wasn't because it's a treaty or human rights violation. It was challenged by the states of Minnesota and Washington on the grounds that the order contravened states' financial rights. And in fact, it's clear that Trump's order would have a financial impact on some states. The legal question, however, is whether Trump's power to prioritize national security outweighs the rights of states to control aspects of their financial independence. I suggest that, especially given the temporary nature of Trump's order, that the final decision will be in his favour.