If you're being prompted for captcha & you're not a splogger, & your blog will stand a manual review to prove it, you can request a review / get in line for the "whitelist" as follows: Blogger Help:

Click the "?" (question mark) icon next to the word verification on your posting form. That will take you to a page where you can request a review for your blog. We'll have someone look at it, verify that it isn't spam, and then whitelist your blog so it no longer has the word verification requirement.

Apparently if you've been asked for captcha & trying to publish remotely (e-mail, 'phone, whatever) then the stuff you submitted from there is being held as drafts until you log in & beat the captcha to make them public. Interesting, & seemingly ongoing / evolving to keep up with the problem.

Update: AdsonBlogs is a false positive, & discusses the phenomenon.

Filed in: blogger, webtech, spam, splogs