'They' cannot just 'send in' the National Guard. The Posse Comitatus Act of 1878 prevents any part of the Army from performing law enforcement functions without an act of congress - in its most basic definition.
That's not how the NG works. Unless federalized, the NG is under the control of the state's governor (Tile 32 USC), and can do whatever state law empowers them to do- particularly law enforcement.
Only Title 10 forces (Army, Navy, Air Force, Marines- to include Reserves and Army NG, Air NG when federalized) fall under the purview of the Posse Comitatus Act. This is why the Coast Guard can also perform law enforcement; in peacetime they fall under Title 14 and become a part of the Navy under Title 10 in wartime.