If I have a blog on Tumblr that is also embedded on my website - will this negatively impact (because of duplicate content) my search engine rankings for either URL?
It is very likely that it will, unless the embedding is done through an iframe. You could try using canonical URLs (see Google reference, SEOMoz tips) to point both URLs to whichever one you want to rank. To be safer, I would recommend showing snippets or a feed of some sort on your website that links back to your tumblr, or just moving everything over to your website via some other platform and forgetting the tumblr. (Yahoo recently bought Tumblr, and based on previous Yahoo acquisitions there is speculation that Tumblr's days may be numbered anyway.)