The President appoints federal judges, including Supreme Court justices, with the advice and consent of the Senate. That means the Senate must approve the President's nomination by a simple majority vote before the appointment process can be completed.
Federalist
Any Article III (constitutional) court (or equivalent state court) can declare a law unconstitutional if the law is part of a case they're trying or reviewing; however, the government would probably appeal the case all the way to the Supreme Court to get a definitive answer.
The US Supreme Court is the ultimate arbiter of constitutionality, and has final authority over questions of constitutionality.
Article III Courts
MEDICARE
Executive
political party conventions