You could use StackEdit (I'm the developer). It's a web-based Markdown editor and it allows you to publish your document (Markdown or converted HTML) on different sites. Amongst others, you can post to Blogger.
I'll rewrite @pajju's answer, because this was the path I chose and I think it works well, although I'll include examples. The source page is this: http://dvdotsenko.blogspot.in/2012/08/markdown-with-blogspotcom-and-bloggercom.html
The basic idea is to write your markdown in HTML mode in a script tag:
<script type="text/x-markdown"> #markdown supported post even with some `code`: > rm -rf / </script>
</body>. For example, this: https://code.google.com/p/pagedown/source/browse/Markdown.Converter.js
The CDATA tags are necessary or blogger's validator complains.
I also threw in a link to google's code-prettify, but directly (unlike the method in the above blog):
Then include a little script to activate everything:
Debugging by writing a small post and hitting preview with the developer console open was necessary. The custom CSS of the template probably also needs some work to make it look decent.
Where exactly do you want Markdown authoring to be available?
If it's for posts that you write, then the modification would need to be to Blogger's editor, not to your template: even if you write in HTML mode rather than Compose mode, Blogger still validates the HTML before publishing the post.
An alternative for posts would be if you want to publish via mail2Post. In that case, it would be reasonable to look for some on-line service that accepts Markdown-formatted content that you provide, converts it to HTML and then send it to an email address that you provide (your "secret-words" address from Blogger).
Another alternative is Windows Live Writer - but I'm not sure if it would support Markdown. And even if it does, AFAIK once a Blogger post is made with WLW, it can only be edited with WLW and not with Blogger's regular post-editor.
On the other hand, if you want Markdown format to be available for comments, then yes I could imagine some 3rd party commenting systems could be integrated, but I'm not sure what they are - perhaps Disqus (definitely works with Blogger) allows Markdown?
It is possible, just follow this link. It does work fine.