It's not clear to me that conservatives want strong state power in general. A small number of hardline libertarians do, but mainstream conservatives have much m

It's not clear to me that conservatives want strong state power in general. A small number of hardline libertarians do, but mainstream conservatives have much more mixed views. The mainstream view wants stronger state control of some things, but strong federal control of other things. Which way it aligns often has more to do with other policy preferences of liberals and conservatives, rather than any consistent view of states' rights on either side. To take one issue on which the conservative/liberal alignment on that question is reversed: conservatives tend to oppose state control over regulation and product liability, and have been strong proponents of uniform federal regulations, which through the doctrine of federal preemption displace state regulations. The reason is that they consider it impractical to have to comply with 50 mutually incompatible auto-safety laws, since cars are not built separately on a state-by-state basis. Instead, they have lobbied (successfully) for the federal government to "occupy the field" with a comprehensive set of automobile safety and emissions regulations, which, through the Supremacy Clause, preempt any state regulation. This has generally been the "conservative" view in both legislation and jurisprudence: conservative federal legislators have been more willing to explicitly preempt state economic and environmental regulation, and conservative judges have been more willing to apply the preemption doctrine broadly. The "liberal" view, meanwhile, has tended to be more in favor of preserving the prerogative of each state to regulate sales, pollution, and product liability within its borders. National security is another one where the alignment is typically the opposite. Many liberals would support a return, at least partially, to the classic decentralized view of armed forces: each state maintains a national guard to be used in case of invasion, and the federal government provides basic coordinating and informational services, but doesn't maintain a large standing army in peacetime. Conservatives generally oppose any significant reduction in the size of the federal armed forces.