File this under Hashtag Facepalm.
I fired up MarsEdit this morning to type up a couple of posts for this blog and found that my password kept getting rejected. It took me a while to realize that the Google Authenticator plugin that I had added to make my logins more secure was (properly!) keeping MarsEdit from connecting. The fix was easy once I figured it out. Here's how you do it:
Log in to your blog and go to your user profile. Scroll down just a bit to Google Authenticator settings. Make sure that "Enable app password" is checked, and then click "Create new password". Copy the password and then click the "Update Profile" button at the bottom of the page. (I missed this step the first time I tried and MarsEdit wouldn't connect.)
Then, in MarsEdit, right-click on your blog and select "Enter password..." from the contextual menu. Enter your regular username and the app password that you just generated. Voila! You can now access your blog securely.