Looks like the Nice Navigation plugin has an unfortunate effect on the load of the main (wp-admin) login page.
My login page is taking 30-40 seconds to load. Googling a fix for this I came across the suggestion that it is likely plugin related. So I disabled all my plugins and have narrowed it down to one of my favorite ones: Nice Navigation!
Without it the load time is 7-9 seconds, with it is 30-40 seconds. Ouch!
I have the plugin installed in the main subsite of my multisite WP installation, running the latest version of WP.
(I really like the plugin and would love to be able to keep it!)