I just lost a lot of time on this, so I'm posting it here to hopefully save others from the same fate.
You cannot create jCarousels when they are not visible. The code that computes the dimensions uses offsetWidth and offsetHeight, which only work for visible elements. I had several tabs that had carousels but the elements were not drawing correctly in the tabs that started out behind - the width of the list was being set to 15. This was due to zeroes being returns for offsetWidth. I have now changed the code to defer population the carousel until it is visible and it is now working.