WASHINGTON — When the police bring the hammer down, whether on Occupy Wall Street in Manhattan’s Zuccotti Park in 2011 or outside the Democratic National Convention in Chicago in 1968, the response from conservatives tend to be fairly consistent: The protesters got what they had coming.

But demonstrations this week over the shooting of Michael Brown, an unarmed teenager, by a police officer in Ferguson, Mo., and the overwhelming law enforcement response that followed have stirred more complicated reactions, with many on the right torn between an impulse to see order restored and concern about whether the crackdown is a symptom of a state run amok.

With broadcasts from Ferguson showing the streets engulfed in smoke as officers looked on wearing military fatigues and carrying high-powered rifles, some prominent conservative commentators and leading Republican politicians began questioning whether the police had gone too far.

These reactions point to a larger debate inside the conservative movement today as Republicans struggle with how enthusiastically to embrace an ascendant strain of libertarianism within their ranks. Senator Rand Paul of Kentucky, a likely candidate for president in 2016, starkly laid out one side of the argument in an op-ed published on Time.com on Thursday.