I would give Priceline a try. This Sheraton downtown is showing a prepaid rate of $97/night for this weekend. This is an excellent hotel near the Kohl. Priceline used to consider this a 3*, but now are showing a 3.5* rating. The Concourse downtown is also a 3.5*, and also has been won on PL. The Concourse has been won for $45. Both are great hotels. The Concourse seems pretty booked, so I'm kinda leaning that you would get the Sheraton...but who knows...
So, here's what I would do:
www.priceline.com
enter Madison, dates.
select "Name your own price"
select 'Madison Downtown" and 3*
Start at $45. If rejected, increase by $5 and add Madison East (sticking with 3.5*). If rejected, add 5$ and select Madison south. If rejected add Madison Southwest. If still rejected, you are out of bids for 3.5*. (you can start over in 24hours). Do not add Madison West, as they also have a 3.5* and you could end up out there.
Now start completely over with a new bid...select Madison downtown, 3*, $45. this time your rebids are only Madison South and Madison Southwest. Again, if denied on rebids, try again tomorrow. It's wise to book a room (as a back up) through normal means, one you can cancel Friday if you get something on PL.
Good Luck, if you have any questions I'd be happy to help.