With four earlier flights cancelled today and essentially no space at all tomorrow, I would expect a lot of people to stick it out and wait around, hoping that the flight goes with them on board. Otherwise, you would be hoping and fighting for space on Wednesday. At this time of year, there just isn't much excess capacity to absorb the stranded.

BTW, when I checked in the afternoon, MSP airport hotels still seemed to have lots of rooms at pretty decent rates. LAX airport hotels seem more problematic. YMMV.