Will blogger let you? THAT is the question.
This is a known issue with blogger, and "probably" the development team is working on it. I found the following information to aid us blogheads in leaving comments.
1. Before attempting to log in, uncheck the "Remember Me" checkbox.
2. Make sure you're running the latest version of your browser. If not, upgrade it.
3. Make sure you have cleared both your COOKIES and CACHE. Directions to do this can be found here: Cookies - Clearing cache and cookies. Once you have done this, shut down the browser. Open it again, and check that the cookies and cache are indeed empty. This is important because the problem seems to be corrupt cookies and cache files. (I think Evalina may have done this and it worked for her.)
4. If the cookies and cache are empty, go to www.blogger.com. Press CTRL+F5 before trying to login.
5. If that doesn't work, try logging into Gmail first, then go to www.blogger.com and try again.
6. If that STILL doesn't work (Is anyone finding this rid-ic-u-lous?!?), try going to http://www2.blogger.com/home.
7. If that doesn't work, try going to draft.blogger.com.
8. If you use IE8 or IE9, try pressing the compatibility button (at the end of the address bar) when you're on the blog page.
9. If all of the above fail, try installing another browser (ie. Firefox, Chrome, Opera, etc) to see if that works. I've heard through the grapevine this has worked for some. For me, this won't work as I use several computers in different locations. I surely am NOT going to install a new browser on each one.
10. You may also want to change your Comments setting from Embed Comments to Pop-Up or Full-Screen until the issue is fixed. To do this go to: Settings --> Comments --> Comment Form Placement --> Select Pop-Up Window (or Full Screen) --> Save Settings. This worked for Niina.
11. I've found that I can leave "anonymous" comments on blogs even if I can't sign in and leave them the normal way. This only works if the blog owner allows anonymous comments. Just be sure to sign your name in the comment box, lol.