Oh yes, you most certainly can! Probably not by using Adsense and the like (unless you are a top blogger), but there is a contest going on called “Blog For A Year” that will award an $80,000 stipend over the year for you to blog on any subject you choose to go with. You can quit your day job and take a shot at professional blogging, which could open many more doors if you had free time for a year to maintain it.
You can learn more about this contest at Blog For A Year, and if you feel up to it, why not enter? Only blogging for 365 days would be quite cool, no?