The sticking point between the two leaders? The Stanley Cup playoffs.
"One place where we have irreconcilable differences will be in the battle between my beloved Ottawa Senators and his Anaheim Mighty Ducks," McGuinty joked Tuesday prior to the governor's arrival.
Speaking Tuesday at a downtown Toronto hotel, Schwarzenegger conceded either team could win the series.
"It's going to be very tight," he said. "We're going to see who is going to win."
Schwarzenegger said he was looking forward to winning a bet that would see McGuinty send the actor-turned-politician one month's supply of Tim Hortons coffee, Ontario wines and a Roots sweater if the Ducks win the Stanley Cup.
"I'm looking forward for his goodies, and I'm sure he's looking to my goodies that I'm sending him," Schwarzenegger said.
The governor took what may be the most direct method to inform Canadians about his three-day trade mission to Ontario and British Columbia by appearing on the pre-game telecast of the opening game of the NHL's Stanley Cup final series.
The politician known as the "governator" - a reference to his role in the Terminator films - appeared with Canadian icons Don Cherry and Ron MacLean on the Hockey Night in Canada broadcast Monday.
The governor's appearance came just before he dropped the puck to begin the game between the Anaheim Mighty Ducks and the Ottawa Senators.
Ontario Premier Dalton McGuinty said that even though he and the governor were set to sign two major agreements this week, the hockey rivalry would remain.
McGuinty continued the hockey theme when he spoke to a delegation of about 50 California business executives travelling as part of Schwarzenegger's first official trade mission to Canada.
"Some of you may be aware of the tune-up game we had last night," he said, referring to the Senators 3-2 loss in the opening game.
McGuinty said California, as the largest American state, and Ontario, as Canada's most populous province, have a lot in common and will work together on issues such as climate change and stem cell research.
Schwarzenegger and the premier will sign an agreement Wednesday that includes low carbon fuel standards for vehicles but stops short of California's tough new tailpipe emission standards, which could hurt Ontario's all-important auto sector.