The articulation political landscape in the US is excessively reductive. "Conservatives", usually referencing social conservatives and often implying Christianity, are
not small government people. They're currently allied with the small government people in a coalition that constitutes the current base of the Republican party, but conservatives and small government libertarian minded people are two different constituencies. They might overlap a bit, you get some religious people with a live and let live mentality or a social conservative who believes that social structures should be enforced by community rather than law, but they're distinct ideologies.
It's like how everyone says liberals are socialist progressives. They're usually not, but the two groups form a coalition that constitutes the base of the Democrat party.