I suspect that Colorado's capitol hill shooter wasn't motivated by historical dates, but July 16 does have some potential significance.
*Ivan IV of Russia murdered (1764)
*Mark Annius Florianus of Rome murdered (276)
The death of an emperor, of course, is followed by the ascension of a new one.
More plausible might be a connection to Emperor Norton I, an eccentric in San Francisco who purported to dissolve the United States on July 16, 1860.