Sen. Lindsey Graham (R-S.C.), who died at 71 last evening from what his office called a "brief and sudden illness," found a way to remain relevant through nearly every phase of modern Washington. The big picture: Graham first rose to national prominence in 1999 as one of the House managers during President Bill Clinton's Senate impeachment trial. After winning election to the Senate in 2002, Graham became one of President George W. Bush's most reliable defenders. Graham's closest political…