Graeme McDowell and Shane Lowry are among the players needing a good performance in the Wyndham Championship to keep their PGA Tour cards and qualify for the FedEx Cup play-offs.
The top 125 players at the end of the week will advance to the Northern Trust Open, with the top 100 then qualifying for the Dell Technologies Championship, 70 for the BMW Championship and the top 30 for the Tour Championship in Atlanta.
McDowell has to finish in the top 35 at Sedgefield Country Club to move up from his current position of 131st, while Lowry is ranked 145th and needs a first top 10 of the season on the PGA Tour.
Only a win or second place would see Harrington reach the top 125 from his position of 199th, although the three-time major winner will be able to play around nine events next season on a medical exemption after undergoing neck surgery in March.
McDowell has missed the cut in five of his last six events, including last week's US PGA Championship, and failed to qualify for the Open for the first time since 2003.
But the former world number four, who is currently ranked 110th, is taking a relaxed approach to the week after making the 90-mile journey from Charlotte to Greensboro.
"I feel like I am focused beyond the play-offs and I am into next season already," McDowell said. "I am not trying to put too much pressure on myself because it is too late in the season to be putting pressure on myself.
"I feel like I have done a lot of good things this season to have nothing to show for it, so it has been frustrating from that point of view.
"I really like the way I am moving and I have got a great end of year schedule. I go back to Europe and I will probably play British Masters and the Dunhill Links and then come back over here and play two or three of the Fall series and try and get some points on the board."
World number nine Henrik Stenson is the only member of the world's top 10 in the field, the former Open champion coming into the event on the back of a tie for 13th at Quail Hollow.
Kevin Kisner, who held a one-shot lead after 54 holes last week and eventually finished seventh, will partner Stenson and Bill Haas in the first two rounds and has finished in the top 10 in each of his last two appearances in the event.