Yes, Trump might be able to declare an "emergency" to build his wall

Is the situation at the border a “national emergency?” That’s debatable. The ideal outcome would be for the elected officials to resolve the matter through a non-emergency appropriation signed into law by the elected president. But the idea that the current situation at the border is an emergency is not far-fetched.

An estimated $64 billion in drugs are smuggled into the United States every year. In 1995, President Clinton signed an executive order declaring a “national emergency” finding that the “actions of significant foreign narcotics traffickers centered in Colombia, and the unparalleled violence, corruption, and harm that they cause in the United States and abroad, constitute an unusual and extraordinary threat to the national security, foreign policy, and economy of the United States.” The order stood long enough for President George W. Bush to extend it in 2004.

My research did not isolate a particular legal standard for “a national emergency,” so it’s possible Trump’s critics could challenge his action in the courts as insufficient on that basis. There’s plenty of violence taking place on both sides of the border in connection with drug smuggling that Trump could cite to invoke the same justification used by Clinton and Bush.