"We should teach them how to respect and be fearful of the law," one netizen wrote on Sina, a popular news website.
If Li's Party membership is suspended, that will mean his political opinions will not count in Party discussions and he will forbidden to vote for Party candidates or run for Party posts during the period.
A suspension of membership is the second-most-severe punishment that can be meted out in the Party system.
Jiang Ming'an, a law professor at Peking University, said the matter will be transferred to the courts if discipline authorities find evidence that Li committed a crime.
"We need a stronger system to regulate the behavior of people who are close to officials," he said. "It's not uncommon for us to hear of cases of officials' drivers or relatives taking advantages of their power.
"Officials should also learn from this case that they have to be vigilant and prevent people who are close to them from committing violations."
In a similar incident in October 2010, Li Qiming, son of a deputy public security director in Baoding, Hebei province, hit two girls while driving, killing one.
Li Qiming was reported to have said at the scene of the accident: "You can sue me if you have what it takes; my father is Li Gang."
Li Qiming was found guilty of the crime and sentenced to six years in prison.