For a generic 'tech' answer, I'd make sure the basic functionality works on IE, if ugly, and concentrate on Firefox and Chrome. (And if you do, Opera and Safari usually work without changes.)
For example, two of our products are (i) A film submission form field and (ii) A schedule for the screenings at the festival.
With basic IE support for both, we noticed <3% of the traffic using IE for the "Submission forms" and ~40% of our traffic to the "Schedules" use IE for a festival in Phoenix.
In hindsight this makes sense. Most people submitting films are the filmmakers or their crew- think Apple's primary target market, hence Safari and FF is what we see a lot of. We've stopped incremental updates for IE on the submission form as long as it remains functional.
However, people looking at schedules are at their enterprise jobs possibly in Phoenix during the day and trying to figure out what films to catch after work. That might explain the high prevalence of IE.
While it is obvious in hindsight, these are not assumptions I would be willing to make without looking at hard data specific to my product. Regardless of whether it's Tech or Filmmaker centric.
Edit: Clarity.
Within the last two weeks code was checked in to allow non-admin level installs, so when that debuts everyone that gets prompted can actually install it.