There are 30-something at-large spots in the tourney, with 30-something reserved for conference winners, so to get in you either need to win the SEC tournament or be among the 30 or so best teams in the country not to win their conference. 65 out of just over 200 teams make it in. In terms of comparison, I believe we had 60+ bowl teams this year out of 118 1-A football programs, so think of making the tournament as about the same as making a bowl game that isn't named after a nut company, tire manufacturer, or .com.
Practically, the standard for a major conference team getting an at-large bid is usually around 20 wins with a .500 or better conference record.