The following video, made by Google explains a bit the concept of AdSense and how to set up your blog hosted on Blogger to provide AdSense ads.
The quick and easy answer is: YES! Earning money with your blog is still possible even with blogs that are not niches.
A typical blog has around 20 to 40 visits per day, a blog that is fed regularly with content should have at least about 50 to 60 daily visits.
However, these numbers can be largely overcome if your blog has good content.