The effect of doing this would be very limiting on the Supreme Court. It would struggle to serve the role that seems outlined for it in the Constitution, which is to serve as a check on the powers of the legislative and the executive branches. Without the power of judicial review invested in the Supreme Court, an important check on the other branches would be removed. Some might argue that the power of judicial review was not clearly invested in the Supreme Court in the Constitution, and that it was only asserted by the actions of the Court itself (i.e. the Marshall Court's decision in Marbury v. Madison or a number of decisions that upheld federal laws previously). It was, however, widely assumed to exist by the Framers of the Constitution (including Alexander Hamilton, who specifically discussed the issue in Federalist 78) and more importantly, has become so deeply imbedded in the American legal tradition that it would represent a major alteration to the interpretation of the Constitution if it were eliminated. Of course, the only way the Court could be stripped of this power is by constitutional amendment.