The Supreme Court used to enjoy great popularity among the American public, but according to recent surveys most Americans feel the Court has become too politicized. The 5-4 decision in Bush v. Gore that ended the Florida recount and decided the 2000 Presidential election is often seen as the most blatant example of a politically split Supreme Court. In that case, Bush sued to stop an election recount that had been allowed by the Florida Supreme Court. The five justices generally seen as right-leaning sided with him, while the four justices generally seen as left-leaning sided with Gore and the Florida Court. A pretty "inconvenient decision," if you ask Gore.
Nowadays, in the post-Bush v. Gore world, a Supreme Court Justice is almost as likely to have somebody throw a tomato at him and yell something about judicial activism as ask for an autograph. The good news for Supreme Court justices is that any decision they make will be met with acclaim and reverence by a portion of the population. You can guess the bad news.