The description of digital natives (sorry, I use the popular terminology) as multi-taskers and concerns that multitasking can lead to disastrous consequences (texting and driving) get a lot of coverage while often lacking a scientific evaluation. The known limitations of short term (working) memory have always been enough for me. Some scientists have taken a more direct approach and are attempting to determine whether a cohort or individuals do have this capability.
Here is a recent description of some researchers work (Scientific American) including an online task you can try.