Right now, Barack is my mainest man and I can’t even get worked up about this.
But I see the longterm negative implications for the Obama administration in this.
Both are correct, and any spell checker should recognize both.
(Also, the spelling with an ‘o’ gets more google hits.)
Also, I just found out that “google” and “spelt” are not recognized.
“Adviser” always looks weird to me (though Firefox “allows” it, and recommends it as a replacement for “advisor”). “Google” as a brand name is OK, “google” with no uppercase is not. Ditto for “Kleenex” and “kleenex”.
“Barack” and “Obama” are both part of my user-defined dictionary, under the assumption that I’m going to need those words at some point in the next four years.
And “spelt” is underlined because it’s not a correct spelling in en-US – you want “spelled” 
Edit: With all the red underlines I was causing on purpose I missed one that I put in on accident.
I cant spell obama and I’m MAD AS HELL ABOUT IT!!!