well that's not right
It is if you think about it in economic and social terms. Liberal ideals like anti-discrimination laws, minimum wage, and higher taxes are all hallmarks of a 'bigger' government, or one that's closer to the authoritarian side. While on the other hand, low taxes, low social welfare, and low federal expenditures are all hallmarks of 'small' government and modern conservative thought.
But like, neither American liberals nor conservatives can be flatly classified as authoritarian or libertarian. Liberals are more libertarian on drugs and social policy (gay marriage, gender identity, etc), while conservatives support stuff like the military-industrial complex and anti-abortion/drug laws. It's a hodge-podge of ideals that doesn't separate out cleanly.
A true authoritarian would be like an unironic communist that legitimately wants the US to revert to complete socialism, and a true libertarian would be like one of those Duck Dynasty nuts who lives off the grid, eat squirrels for dinner, and have a bunker full of guns and MREs.
Poll