I'd guess 7.62x39 or 5.56; maybe some of each, depending on from where they recruit people stupid enough to invade the USA.
All the militaries, of all the nations in the world, including reserve military, paramilitary, police of all sorts, every government critter who is trained and armed, in all nations combined -- they total about 75 Million.
Substantially less than that total are stupid enough to volunteer to invade the USA.
In the USA, there are about 150 Million men, women, and children, armed or in possession of between 500 Million and one Billion rifles, pistols, and shotguns, with probably a thousand rounds average for each of those. Of those, 17.4 Million are military veterans, and triple or quadruple that number were taught to shoot and hunt by veterans, or by other accomplished shooters, hunters, etc.
Lots of these people hunt and fish, and have the proper clothing and equipment for the weather and terrain in their area, and many who are prepared for the elements in multiple areas.
Other than a few thousand government slugs, and a few million worthless commie fags, who hate us enough to join the enemy, I figure most Americans will stick with their own side.
Pretty sure the blue hats shoot 5.56. IIRC, that was the reason we dropped the 7.62 and moved to the 5.56 was to match with NATO and the UN.