Supreme Court Justices are appointed by the president and confirmed by the Senate. In theory, this procedure allows both the executive and legislative branches to have some power over the judiciary and thus "check" the judicial branch's power.
The President is not mandated to carry out the orders of the Supreme Court. The Supreme Court does not have any enforcement power; the enforcement power lies solely with the executive branch. Thus, the executive branch can place a check on the Supreme Court through refusal to execute the orders of the court.
