New research suggests that we are not able to mulitask well:

Recognizing new information in your surroundings and incorporating it into your view of the world is referred to as “encoding,” while reacting to stimuli and making decisions is termed “response selection.” They’re distinct processes, but they utilize some of the same parts of the brain, so it’s possible that the brain can have trouble if asked to perform both of these processes at once or in very close succession. In this study, the researchers used fMRI data to determine whether there is a common bottleneck for both perception and decision making.

So what does that mean?

So, not only does doing two things at once decrease your speed and accuracy, but it appears that one bottleneck may be responsible for this effect even if the tasks are different. Of course, this is probably not the only neural bottleneck we have; other structures, alone or in combination, likely limit one or more different processes as well. However, this is good evidence that very different cognitive tasks may interfere with each other, thanks to limitations of specific areas in the brain.