Can the President decide if a law is unconstitutional?

The President has the enumerated power to make treaties, which are U.S. laws. Two-thirds of the Senate must consent. Note that consent from both houses of the legislature is not required, and also that the judicial branch gives significant deference to the Executive Branch when interpreting laws regarding foreign policy because it is a power enumerated to the Executive. Also note, the several executive departments, such as EPA and Homeland Security, make code which is effectively law because the Legislature delegates such authority to the Executive.