@bobbym46,
This is an intro organic chemistry course and I'm pretty sure your instructor wants you to learn the "textbook" reactivity. In that sense, you are indeed right that with a strong base and a tertiary electrophile you should expect E2 products. So the two products that you drew are indeed the two and only "textbook" products that would be expected. I am an organic chemistry professor who has been teaching this material at university for over ten years to undergraduates: if my question were for students to list all the elimination products in the reaction that you showed, I would expect them to show the two products you found.
Problem is I don't know what the complete question in your problem is, and what your instructor wants you to write. As orgopete nicely describes, this kind of reaction is textbook E2, but it is well known (through fun experiments such as the one he describes) that this picture is a crude over-simplification and that a many reactions with tertiary electrophiles have much more E1 character (to the point of even forming the carbocation) than what can be discussed in an intro course.
So what am I saying? I don't know what your prof wants you to write but you've covered all E2. If that is not a complete enough answer for your instructor, then you can look into substitution products (through SN1?) or carbocation rearrangement products (the initially formed C+ in your problem shouldn't rearrange as it can't form a more stable one, but maybe that's still what your instructor is looking for when asking for ALL the possible products?)
Hope this helps.
@orgopete
That is a cool experiment. Way back when I was an undergraduate, we had a half-semester of looking into classic physical organic chemistry concepts. I don't remember exactly what the experiment was, but we had something similar and I just remember that it completely confused me at that time as I just couldn't appreciate that the complexity is what made it fascinating.
That whole half-semester was a lot of fun as the professor's intent was mostly to debunk some of those classic "myths". I remember we looked into why it makes no sense to propose the occurrence of real free carbocations in solution, why most SN1 reactions are only first-order because the second step is at saturation and how you can make certain SN1 reactions completely second-order, how emphasizing the quantitative treatment of pKa values is pretty terrible when trying to predict the reactivity or organic compounds outside of (1) aqueous solutions at (2) very low concentrations, etc. It was a lot of fun! Nothing I would do in my intro classes with my undergrads though.
As an aside, I do agree that the product distribution can, minimally, depend on the tiny differences of acidity when using hindered based like KOt-Bu, but would argue that the steric effects are by far the dominant factor.
Cheers!