Public support means the maximum upkeep which is paid from the public budget. It's defined by population in billions multiplied by 3 (more details in the chapter For mods, but they are irrelevant for a normal gamer).
The upkeep costs are first covered by the public support. When the upkeep is higher than the public support, it turns red and your revenues (seen as "Change" in NaviCon) decrease to pay for it. If the state finances (seen as "credits") turn red, you can't build any more ships until you pay off your debts.
3 is the factor POPSUPPORT_MULTI defined in Constant.h and can't be changed except when compiling the game. In BotEDoc.cpp public support is defined like this: AddPopSupportCosts ((UINT) fCurrentHabitants*POPSUPPORT_MULTI).