So let's say an admin user creates a new site in the network. Next, he needs to create new posts and pages and activate plugins, update the sidebar and so on. So maybe the site will be broken (under construction).
Here you got a small plugin. If you don't (or can't) use a plugin, this should - in theory - as well work from within your functions.php file. Just leave the plugin comment header out.
<?php
/** Plugin Name: (#90328) Login with E-Mail address */
function login_with_email_address( &$username ) {
...
I had to review an edit and I'm not sure how to handle it. Maybe someone can have a look at this one: » http://wordpress.stackexchange.com/a/23830/32946