From what I understand using GET to submit usernames/passwords is a security issue because the username/password are part of the URL which can show up in browser history.
That's not the only issue. Using GET for situations where the user is submitting data opens up your application to CSRF vulnerabilities.
For example, I could embed
<img src="http://yoursite.com/login?username=something&password=somethingelse">, which may log visitors on my site out of your site due to the call to the login handler. This specific example depends on implementation, but other attacks can be made. There may be cases when an attacker wants users to be logged in to their account.
Besides that, other loggers on the way (your ISP, etc) may log this for a longish period of time. Of course, the same can be said about POST request, but usually the full request dtails won't be kept for long.