Any kind of armed conflict, including war, is a tool of politics. While theoretically speaking, no armed militia will ever be able to beat the US Army, that's not the question. The question is, will an armed resistance change the politics of the conflict enough to not engage in it.
For example, let's say you want to send the army or police to (let's say) take control over some city and implement a curfew. If the populace is armed and decides to oppose you, your calculus now includes whether it's worth killing many people to get your aims. That might make it politically impossible to do, either because it's now no longer worth it, or because the army itself might resist you.
Obviously those are extreme scenarios. You can see many, many cases where a small armed populace managed to "win" against a much larger army, because unlike what some people think, war is very rarely an all-out "get your way at any cost" affair.
For example, let's say you want to send the army or police to (let's say) take control over some city and implement a curfew. If the populace is armed and decides to oppose you, your calculus now includes whether it's worth killing many people to get your aims. That might make it politically impossible to do, either because it's now no longer worth it, or because the army itself might resist you.
Obviously those are extreme scenarios. You can see many, many cases where a small armed populace managed to "win" against a much larger army, because unlike what some people think, war is very rarely an all-out "get your way at any cost" affair.