I'm not a frequent blogger, so have only been bitten by this issue today - but checking the internet for clues it seems I'm not the only one. I wrote a long blog post in Live Writer and then tried to upload it, only to see this error message come up...
Being a geek I looked into this further and found that it was an issue with how Windows Live Writer authenticates (i.e. logs in) to Blogger. Google have disabled the mechanism that WLW was using, and so at this present moment (28th May 2015) you can't use WLW with a Blogger account. Pants.
There is currently no workaround (for WLW that is) - you simply cannot use it.
If you're on the Blogger platform you can use their tools to blog with (that's what I'm using here), or try out some other blog tools on the web. For now I'll limp along with the Blogger UI, it's OK - but nowhere near as easy to use as Windows Live Writer. Sadly it seems that Microsoft are no longer maintaining WLW, so you may be waiting a long while for a fix.