Both sides have top-loaded their line-ups for what promises to be an intriguing last day at Medinah Country Club, where birdies have been plentiful on a tree-lined layout virtually shorn of rough with greens running at lightning speed.
The US need only four-and-a-half more points to regain the Cup after building a commanding 10-6 lead in Saturday afternoon's fourballs, while holders Europe require eight more points to retain the trophy.
"We just want to win each segment," said US captain Davis Love III, whose tactics have so far been successful with his four rookies performing superbly and the entire team relishing the pressure cooker atmosphere of the biennial competition.
"We want to go out, have some fun and not really think about the outcome. We have one more day to go, and we'd just like to go out and play. Our guys, they all want to win a point."
Love will send out Masters champion Bubba Watson first, against Englishman Luke Donald, US Open winner Webb Simpson next, against Englishman Ian Poulter, and red-hot Keegan Bradley third, against world number one Rory McIlroy.
Veteran Phil Mickelson, Cup rookie Brandt Snedeker, long-hitting Dustin Johnson and Zach Johnson fill the next four slots, and will meet Justin Rose, Paul Lawrie, Nicolas Colsaerts and Graeme McDowell respectively.
"We didn't really look at where the pairings would fall, the match-ups would fall or where the final point would fall," said Love. "We just looked at who wanted to go where.
"There was a group of guys that like to play pretty fast, and there's a group of guys that are more comfortable playing later in the day."
American world number two Tiger Woods will anchor the singles order having lost all three matches he played this week in tandem with Steve Stricker, who will tee off in the 11th and penultimate spot on Sunday.
"Tiger is used to teeing off at 1:00 or 2:00 in the afternoon, that's kind of his usual time on weekends," Love explained.
"So we looked at a lot of different things. I needed some stability, I think, in different spots. You needed guys like Tiger and Strick down towards the end."
While the US team had a pep talk from former President George W. Bush and his father, former President George H.W. Bush, on Saturday evening, the Europeans know their inspiration can come only from a fast start on Sunday.
"We are trailing by four points. We have to put the players that are playing well out there," said Europe captain Jose Maria Olazabal. "If we want to win this match, we have to take their big guns down.
"Well, that's what they've done. They've put all the players that have been playing really well this week up there (at the top), and hopefully tomorrow will be a different day.
"I think we haven't had any momentum until the last couple of matches today. If we make a few putts on the green, I think we're going to be a little bit closer."
For Europe to triumph on Sunday they would have to emulate the 1999 US team, which pulled off the biggest ever Cup comeback after trailing 10-6 going into the last-day singles at Brookline.
Asked if he had any special feeling about the challenge facing his team, Olazabal replied: "I believe that it's not over. That's what I learned from Seve (Ballesteros), and that's what I'm going to try to pass to the players.
"There are 12 matches to be played tomorrow. Of course we have a tough task ahead, but it's not over; as simple as that. Let's go out there and play our socks off."
RYDER CUP SINGLES MATCHES (UK times)
17:03 - Bubba Watson v Luke Donald
17: 14 - Webb Simpson v Ian Poulter
17:25 - Keegan Bradley v Rory McIlroy
17:36 - Phil Mickelson v Justin Rose
17:47 - Brandt Snedeker v Paul Lawrie
17:58 - Dustin Johnson v Nicolas Colsaerts
18:09 - Zach Johnson v Graeme McDowell
18:20 - Jim Furyk v Sergio Garcia
18:31 - Jason Dufner v Peter Hanson
18:42 - Matt Kuchar v Lee Westwood
18:53 - Steve Stricker v Martin Kaymer
19:04 Tiger Woods v Francesco Molinari
- Tiger Woods
- Dustin Johnson