I don't think there is an EXACT equivalent to the Henry here. There are several reasons which I'll list below:
1) Americans (and perhaps Canadians too) have a strong preference for upright-style machines.
2) Despite the recent shifts, wall-to-wall carpeting remains popular in US houses.
3) Wet/Dry vacs such as Rigid and Shop-Vac have a stranglehold on the market for "industrial use" machines.
4) Shark dominates the US market with near-40% market share.
These types of machines wouldn't really cut it for most US houses and their purpose is met by other machines.
