European captain Paul McGinley will leave it to the last minute to decide on his Ryder Cup wild cards, admitting "something spectacular" could yet influence his decision.
Scotland's Stephen Gallacher is the only player who can move into the automatic qualifying places by finishing first or second in the final counting event, this week's Italian Open.
But even if Gallacher fails to dislodge Graeme McDowell from the team, the winner in Turin on Sunday or even in Boston on Monday may make a compelling case for one of McGinley's three wild cards to be named on Tuesday.
Although the Deutsche Bank Championship does not count for qualifying, the likes of Ian Poulter and Luke Donald will be keen to impress in the second FedEx Cup play-off event.
"There is an opportunity this week for the guys to play well in the last counting event when the spotlight is on them, which will be huge for those players," McGinley said.
"Even if they don't qualify automatically there are a few players here who could win or do very well and really give themselves the best possible chance of a pick.
"I want to see guys bursting over the line this week.
"I want the Ryder Cup to be something they gravitate towards and something that excites them to the point where the golf they produce elevates them and pushes them towards that finishing line, just like Jamie Donaldson did last week (winning the Czech Masters to seal his place).
"It was pressurised, it was exciting and that's what I want to see from the guys here this week and the others who are playing in America.
"If something spectacular happens either here or in America this week then I will consider it. A win here would be hugely significant in this kind of spotlight at the last counting event.
"It would be massively significant in terms of pushing someone over the line."
McGinley admits he faces a tough task in making his selections on Monday, with three heroes from the 'Miracle at Medinah' in 2012 - Donald, Poulter and Lee Westwood - all having to rely on a wild card.
Gallacher knocking McDowell out of the team would complicate matters further, while the likes of Joost Luiten and Francesco Molinari would boost their chances with a win in Turin.
"This is the toughest part of my job so far since I was appointed," McGinley added.
"All the ex-captains who I have spoken to have told me this is the most difficult part because you are going to have to make phone calls to some guys who are friends and tell them that they are not in the team.
"It will be tough but I am not alone because I have two very experienced vice-captains in Des Smyth and Sam Torrance who are there to help me.
"We will spend all day on Monday discussing it and then we will watch the golf from America and make our announcement on Tuesday."
McGinley knows from experience what the players in Italy are going through, as he sealed his place on the team in 2004 by finishing joint sixth in the final event.
"I can understand the pressure the players are under and I can relate to it," the Dubliner added.
"There is no doubt that the pressure I was under in 2004 and the way I pushed myself over the line to make the team helped me play my best Ryder Cup in Detroit that year."