A self-adjusting bracket assembly includes a bracket, a clip housing, and a clip. The clip housing is supported by the bracket and includes an anterior side opening, a superior side opening, and a cavity in communication with the anterior and superior side openings. The cavity includes at least one housing ramp surface and at least one housing support surface. The at least one housing ramp surface extends at an angle relative to the at least one housing support surface. The clip is received within the cavity and is configured to move within the cavity from an uninstalled position to an installed position.