Very important. The following cases were decided by 5-4 vote of Supreme Court Justices. A single person kept the law from being decided the other way, think about that:
Planned Parenthood v. Casey (1992) (affirming Roe v Wade)
Bush v. Gore (2000) (FL vote recount)
District of Columbia v Heller (2008) (2A rights)
Citizens United v FEC (2010)
National Federation of Independent Business v Sebelius (2012) (Obamacare)
Burwell v. Hobby Lobby Stores (2014)
Looks like it took FIVE - not one.