So tumblr finally showed the true colors and went deep with the latest censorship announcement. All porn to be stopped in less than two weeks.
I logged into to tumblr and found the info on how to export my blog, pics and such. It took hours for it to finish collecting all my stuff and make it available as a download.
You may be able to import your tumblr blog into another platform like a wordpress site or wordpress multi-site, even without downloading a backup – but only if the API thing is working at the time, so I would start the backup / download process as soon as possible, and then move on the API import and see if that works.