Off the top of my head (without any research whatsoever) I'd say that three factors stifled the Amiga in the US.
Firstly, the NES. It was a huge success in America, much bigger than in the UK, and even more powerful machines didn't really stand a chance against it - I think even the Genesis had a pretty tough fight to begin with. Compare it with the PlayStation/PS2 - despite the DreamCast, XBox and Game Cube all being more powerful, and in many instances having better (if fewer) games, the Sony machines seem to win every time.
Secondly, the PC. The PC was never very big in the UK outside of the office, but I think it established its dominance in US hacking circles fairly early on. I could be wrong, but it seems that whilst the Brits had the Dragon, Speccy, BBC, etc, the Americans had IBMs, or had C64s and then progressed to IBM compatibles.
Thirdly, Commodore. The desktop wedges (500, 600 and 1200) were heavily marketted in the UK as games machines. In the US, the onus was very much on the big-box machines (1000, 2000, etc) as business and multimedia workstations. You can see the evidence for this on eBay - big-box machines change hands for a few dollars on eBay.com, but tend to fetch stupid prices on eBay.co.uk. Similarly, 1200s were allegedly extremely rare in America, and don't tend to appear on eBay.com at all. To put that into perspective, I recently gave one of my 1200s away - they tend to be very cheap at car boot sales.
The big-box machines cost a fortune, hence the old joke that the A2000 was so called because it cost £2000; the desktops were cheap.