It's not like ICE can just roll into a state capitol and stop elections.
How many folks would be required for that at each polling place? Ten? Fifty? There are 3500+ counties in the US, usually with multiple polling places. You'd need tens of thousands, if not hundreds of thousands of troops for that.
And that's a lot of armed thugs. Likely the National Guard would need to be federalized, but I find it hard to believe that commanders would follow such illegal orders.