I did a little research on the at-large teams from the past 4 years who were seeded 10 or lower. There were 30 such teams, 22 from power conferences, 8 from mid-majors. I looked at the Nitty Gritty details that the committee received and looked for trends. Here is what I found.
29 of the 30 teams had at least 6 combined road/neutral wins. Bubble teams currently at 5 include Connecticut, Mississippi State, Washington, Miami, FL and Central Florida. Bubble teams currently at 4 include Texas, Illinois, South Florida and Colorado State.
20 of the 22 power conference teams had at least 3 top 50 RPI wins. 7 of the 8 non-power conference teams had at least 2 RPI top 50 wins. Bubble teams currently short of this criteria include Northwestern(2), Miami, FL(2), Mississippi State(2), LSU(2), BYU(1), South Florida(1), Arizona(1), St. Louis(1), VCU(1), Iona(1), NC State(1), California(0), Washington(0), Oregon(0), Drexel(0). In 2011, UAB and Clemson each had zero, so the expansion to 68 teams may have loosened this criteria.
28 of the 30 teams had at least 6 RPI top 100 wins, 29 of the 30 had 5, all had 4. Bubble teams less than 6 include St. Mary's(5), BYU(5), South Florida(5), LSU(5), Iona(5), Iowa State(4), Texas(4), Arizona(4), NC State(4), VCU(4), Drexel(4), Washington(3), Miami, FL(3), Central Florida(3), Oregon(2).
The RPI of 51 for VCU was the lowest in the last 4 years by a mid-major, with 44 being the 2nd lowest.
Major conference teams with RPI's of 61, 63, 64 and 67 have made it in the last 4 years, essentially one above 60 each year. Coincidentally, no major conference team with an RPI in the top 50 has not been selected in the past 4 years, although there were 3 the year before and 4 the year before that, all higher than 38th.
Although top 25 RPI wins are not on the Nitty Gritty, 25 of 30 teams had at least 1 of those.
I know this isn't a huge sample size, but it gives some guidance. It appears a team with a higher RPI can get in if they meet or excel in all other categories. A team with a lower RPI can usually have one category slip-up.
Still a long way to go, but for some, time is running out.