Source: H. Graetz, History of the Jews, volume II (Philadelphia: Jewish Publication Society of America, 1893) 108.
“These despotic acts of Herod were not calculated to make him beloved by his people. He was perfectly aware of their ill-will towards him, but as he could not crush it, he at least sought to make it harmless. Thus he insisted upon all subjects taking an oath of allegiance, resolving to punish severely those who would refrain from doing so. The Essenes alone, who disapproved of oaths, were exempt; he had no cause to fear in their peaceful, contemplative lives; on the contrary, he warmly approved of such subjects, who would submit without murmuring to any law that he might choose to make. Those amongst the Pharisees who were the followers of the peace-loving Hillel seem to have taken the required oath without hesitation, but the followers of the sterner Shammai stubbornly refused to do so. Six thousand Pharisees in all refused to take the oath of allegiance, and to inflict corporal punishment upon so great a number appeared, even to Herod, a serious matter. So he heavily taxed the refractory, amongst whom was the wife of his brother Pheroras, an ardent devotee, strange to say, of strict Phariseesm.”
Graetz talks elsewhere about the Shammai school’s rebellious streak. The way he tells it, look for a political revolution, and you’ll find that Shammai was behind it in some way, shape, or form. According to Graetz, the Shammaites regarded Herod as a horrible Idumean, and they didn’t think much of converts. The Hillelites, by contrast, welcomed Gentile converts with open arms.
I’m not sure where Graetz gets his information, since he doesn’t cite his sources. Josephus doesn’t mention Shammai, and he’s a big source of information about Herod. He also tries to distance the Pharisees from political revolution, since he’s promoting them for power after 70 C.E. (according to one point of view). Does rabbinic literature discuss Shammai’s revolutionary positions? I’m not sure.