The U.S. Supreme Court can decide the fate of the president. In 1974, the Watergate tape case brought down President Nixon. Decided on July 24, he left Washington for the last time on presidential Marine One on August 9 (the helicopter is now at his Yorba Linda museum).
No more direct or dramatic example of the power of the Court exists than the Supreme Court decision in Bush v. Gore in December 2000 when the Court stopped the Florida recount and in effect allowed the electoral votes to be awarded to G.W. Bush.
And although no Affordable Health Care bounce is visible in the polls, President Obama was a big winner from the 5 to 4 decision on June 28, 2012 to uphold his signature legislation as constitutional. A loss would have likely been a blow that could well have been very difficult for him to overcome.
Although the Court is the least democratic branch, it often has the greatest impact on the functioning of our democracy.