With the biggest guns all in a group of riders who are one second behind Belgian leader Jan Bakelants after the three Corsican stages, the winning team are almost certain to take the overall lead.
The rider taking the coveted jersey will be the one who is best ranked after the third stage - in Sky's case, Norway's Edvald Boasson-Hagen.
Sky are among the top contenders for the fourth stage, a collective 25-km effort against the clock in the streets of Nice.
Their hopes took a minor knock when Ian Stannard and Geraint Thomas crashed in Saturday's opening stage but the former was spotted at the front of the peloton on Monday.
The Welshman, though, sustained a small pelvis fracture and looked in agony at the back, hanging on for dear life.
The distance, however, is short so the British outfit may not be hampered too much from Thomas's woes.
""I am definitely going to give it a good go. My mum doesn't want me to but it's the tour, it's not your average race and I am definitely going to keep fighting," Thomas said, brushing aside the idea of quitting the race.
Asked about the time trial, the team pursuit Olympic champion said: "It is really frustrating. I was really looking forward to that and we have got a strong team for that but it has just turned into a matter of survival for the first few days."
Rivals and team time trial world champions Omega Pharma-Quick Step have also had problems.
Double individual time trial world champion Tony Martin of Germany suffered concussion and a deep wound to his elbow on Saturday, while Mark Cavendish has had bronchitis.
Martin, however, finished Monday's hilly stage in the leading bunch, suggesting he could be fitter than expected on Tuesday, and French time trial champion Sylvain Chavanel looks in ominous form.
Team Garmin-Sharp, also time trial specialists, have a chance to put Briton David Millar in yellow 13 years after the Scot claimed the overall lead after the prologue in Poitiers.
"I'd say it's between ourselves, BMC and GreenEdge as the favourite teams," Garmin-Sharp manager Jonathan Vaughters told Reuters.
"Sky will do very well but their biggest engine Geraint Thomas is injured. But hey, they could win, too."
Team Saxo-Tinkoff will be looking to limit the damage for Alberto Contador.
"We have a very strong team and I hope to do a great time trial," the Spaniard said. "We have been training together these last days and the feeling is very good."
According to Vaughters, barring major incident, no team should suffer unduly.
"The time gaps will be very minimal," the American said.
Should BMC prevail, Australian Cadel Evans, the 2011 champion, should take the yellow jersey.
- Sports & Recreation
- Geraint Thomas