They changed in 2006. Now they guarantee a slot to regular season conference champions who don't make the NCAAs because someone else won the conference tournament. You don't HAVE to have a winning record, but they aren't choosing teams that don't. There are usually ~11 auto qualifiers, leaving around 21 spots in the 32 team field for at large teams. Here are some facts/figures from the last four NIT fields.
Number of at large teams: 21, 22, 19 and 20
Number of Power Conference at large: 12, 13, 11, 8 (includes the Big East through 2013 so St. John's & Providence count for that year, but not the American since then which had UConn last year)
Average RPI of at large: 77, 73, 64, 67
Average RPI of power conference at large: 80, 78, 67, 74
Four year RPI average of all teams: 70.6
Four year RPI average of power conference teams: 75.9
Average wins of at large: 19.8, 19.7, 20.8, 20.9
Average wins of power conference at large: 19.4, 19.2, 19.6, 19.9
Four year wins average of all teams: 20.3
Four year wins average of power conference teams: 19.3
Weakest at large power conference teams by year:
2012 by RPI: Iowa (131)
2012 by wins: Iowa, Minnesota and Tennessee, all with 17
2013 by RPI: St. John's (94)
2013 by wins: St. John's with 16, Providence and Baylor with 17
2014 by RPI: West Virginia (90)
2014 by wins: West Virginia with 17, five others had 19
2015 by RPI: Vandy (113) then Arizona State (102)
2015 by wins: Arizona State with 17, Alabama with 18
For reference we are 140 in the latest RPI with a 13-15 record. To even get in the conversation, we probably need to go 4-1 in the next five to get to 17 wins. No clue what that does to the RPI, but if you presume the loss is on Saturday of the SECT to someone like Kentucky or TAMU, that means we would win at Ole Miss, at home against Auburn, then on a neutral site against two middling SEC teams. Again, I have no idea how much that moves the needle at this point in the season.