Must log into Mojang account in Internet Explorer before launcher

When using a question-secured Mojang account, one must log into it first in Internet Explorer before the launcher can complete the login. If a login has not been completed in Internet Explorer, the launcher login dialog hangs indefinitely. Additionally, it seems that the login must occur in Internet Explorer; logging in from Firefox has no effect on the launcher. (I haven't tried Chrome.)

Presumably, this is due to an inability of the launcher to prompt the user with their security question.