raimius said:I really don't see how people think protecting a negative liberty would lead to more government power...
Equal treatment (don't discriminate) is a right that seems to fall within your meaning of a "negative liberty". To achieve equal treatment in education, the federal courts assumed powers to order student busing, school staffing and funding, and school construction and renovation. Such powers had previously been local and state in nature.
Most local schools are funded by property taxes and local residents either vote on school funding or elect representatives who vote on school funding. However, I have lived in a city whose schools were under federal court supervision and a federal judge simply ordered an increase in local taxes to provide more money for the schools. Thus, protecting the "negative liberty" of anti-discrimination led to the rather unpleasant exercise of government power to impose taxes without representation.