Negative interest rates are easy for the US Treasury to institute. They can only offer t-bonds that can be redeemed for less than the bonds were purchased for.
Businesses and such will have to go along because there's nowhere to store $10-$100 billion dollars in short-term, cash-equivalents. I'm willing to be that most companies auto-renew their short-term t-bonds at market rates. Thus, if negative yield t-bonds went on offer, they'd be bought up by the tens of billions. It would be news-worthy, but companies would be unlikely to really act any different as a result.
Long term, some companies might move currency to the treasury of another country, but that introduces risks involved with exchange rates which would greatly overshadow any potential interest gains.
If you look at the €/USD over the past ten years, it's pretty clear that storing USD in Euros to earn 0.2% in interest is for fools; the lowest ratio (ever) is like 0.87 and the highest was 1.58, and these two events occurred only 8 years apart. Even the month-to-month changes are rather dramatic. American companies doing business in USD are going to continue to hold USD regardless of negative interest rates.
