As of today, the Gophers look to be safely in the NIT. A win against Wisconsin tonight would bump them up to a 1- or 2-seed, however a loss really wouldn't hurt much, if at all. What would hurt is a loss on Sunday against Penn State, or a first round Big10 tournament loss to a bottom-feeder Big10 team. Unless Northwestern finds a way to beat Iowa in Iowa City, the Gophers need to win just one of their remaining two games to avoid a day-one game in the Big 10 tourney.
If today's standings hold, Minnesota would draw Indiana in the #7-#10 day-two matchup. There is an outside chance of catching Michigan for the #9 seed, but that would require Gopher victories over Wisconsin and Penn State, and a Michigan loss against visiting [last-place] Rutgers.
Indiana currently holds a tie-breaker over Illinois, and finishes the regular season at home against the Spartans. The only way the Illini can gain the 7-seed would be winning their final game at Purdue and a Michigan State win over Indiana.
There are currently 11 conferences where the regular season winner is a lock for an at-large bid. That leaves 20 potential NIT auto-bids (Ivy League regular season winner gets NCAA auto-bid). Assuming the favorite will win in slightly more than half of those conference tourneys, we would expect there to be between 8-10 auto bids from these 20 tournaments. Most of these teams will fall to the 7- and 8-seeds in the NIT bracket, with the possibility of one or two sneaking a couple seeds higher.
1's: Davidson, Connecticut, Stanford, UCLA
2's: Purdue, Pittsburgh, Richmond, Miami (FL)
3's: BYU, Kansas State, Central Michigan, Minnesota
4's: Rhode Island, Saint Mary's College, Seton Hall, Michigan
5's: South Carolina, Florida, Alabama, Wyoming
6's: Tennessee, UTEP, Memphis, Louisiana Tech
7's: Clemson, Valbaraiso, William & Mary, Albany
8's: Sacramento State, Georgia Southern, Charleston Southern, North Florida
FFO: Yale, Massachusetts, Illinois State, California
NFO: Toledo, Bowling Green, George Washington, Kent State