I think you’ll find that most jobs these days that get into the interactive-experience range of things really aren’t looking for “designers” as most people in the ID field normally think of them.
I mean a great example is that of the web designer. When I started school for design you could be a web designer just by knowing HTML tables, photoshop, and a handfull of Javascript. But within five years that whole notion was completely blown out of the water to the point that most graphic designers or industrial designers could not even qualify for the basic requirements of the job posting.
Just look at any of the job postings for entry level gigs at Yahoo or other well known tech companies. They might say that they are looking for an “interactive designer” but look through the requirements and it becomes clear that they are really looking for a technically proficient programmer with a sense of style. A recent web design job required: XHTML, XML, AJAX, Ruby, CSS2, RSS, Javascript, Java, PHP,.ASP, and MySQL.
For higher paying levels they wanted experience in C++, C# (C-sharp from Micro$oft), and other .Net experience which essentially means that they are looking for someone who graduated from a Computer Science or Electrical Engineering program and not someone who went to art school for a bachelors degree.
If you are really looking to get involved in the “tech” end of things and work in interaction then you really need to look at moving away from ID and more to CS. But ideally you do want a balance of the two so an undergrad in CS and a masters in ID would probably be a good way to go.