To my knowledge, the US had no direct equivalent to the Home Guard during WWII. During the war, people were more concerned with the possibility of a Japanese invasion than one coming from Nazi Germany. (The Japanese successfully launched a small number of bombing raids against the US, although from what I know, they were pretty ineffective.) Also, there was more fear of Japanese sabotage during the war than any sort of German sabotage.
The closest we've ever had to the Home Guard would be some sort of combination of the US Coast Guard (for coastal security), the National Guard (state militias for last-ditch national defense), and state and local law enforcement organizations.
In all likelihood, National Guard units would've been deployed right alongside regular US Army units in every single major theater of combat during WWII. That said, I highly doubt all National Guard units would've been deployed at all times; some probably would've been at home in case of some national emergency.
If I may, what did you have in mind? With some more detail, I might be able to help direct you in the right direction.
