There is no winning record requirement to make the NCAA tourney - or even the NIT.
As of today, ESPN projects only four teams getting from the SEC: Kentucky as a 3 seed, Auburn as a 6 and Florida and LSU as 9s. ESPN has Arkansas and South Carolina among the batch of first teams left off the bracket. I would presume Mississippi State would be close also.
CBS also has only four in the NCAAs: Kentucky as a 3, Auburn as a 5, Florida as a 9 and LSU as a 10. Arkansas and Mississippi State are the top bubble teams.
I think the league gets five at max - and that would require Arkansas or Mississippi State to win a few games in Nashville.
If you care about the NIT - some do, some don't - the problem with the SEC getting so few teams in the NCAA Tournmant means there's a glut of SEC teams available for the NIT field. But that's only a 32-team bracket, and I can't imagine 8-9 teams from one conference will make the field. If the SEC were getting six or seven teams in the NCAA, then a 16-win Missouri team ... or Ole Miss ... or Georgia would have a better shot at the NIT. Maybe not this year.