I like this idea. You wouldn't even need to make it only work for a single login. Let it live for a year or forever. Automate the bookmark procedure for them

I like this idea. You wouldn't even need to make it only work for a single login. Let it live for a year or forever. Automate the bookmark procedure for them as well, so their bookmark for your site (https, of course) would automatically log them in, as it would contain a very large random string that identifies them. For extra points on sensitive sites, tie that random string to their IP address, so it only works from the IP address they were at when they first clicked it. If they click it from a new IP address, an email is sent, asking permission to whitelist that IP address for them as well.