But as he prepared to open a training camp in Toronto later this week, Triano wondered Monday if he may soon be facing the opposite problem.
The camp, which opens Friday at the Air Canada Centre, will include NBA players Tristan Thompson, Cory Joseph, Andrew Nicholson and Joel Anthony. Recently drafted Kelly Olynyk and first overall pick Anthony Bennett will also be with the team, though neither will participate due to injury.
Phenom Andrew Wiggins will not be with the group, opting instead to focus on preparing for his freshman season at Kansas. Still, there will be plenty of competition for playing time among the camp's 18 attendees.
And perhaps some tough decisions for general manager Steve Nash and Triano, who returned to the helm a year ago after coaching Canada from 1998 to 2004.
"I said to Steve, 'Man, this is not an easy job … it used to be we had hard time convincing NBA players to play for our country,'" Triano said at a news conference. "(Now in the future) we're going to have to cut an NBA player off of our Canadian national team."
"Steve says, 'That's great,' I said, 'Not for me,' I don't want to be that guy," Triano said with a laugh. "That's where we are."
Nash, himself a star player with the Los Angeles Lakers, calls it Canada's "golden age of basketball."
The team is using the camp to prepare for the Aug. 30-Sept. 11 FIBA Americas Championship in Venezuela, where the top four teams will qualify for the 2014 FIBA World Cup in Spain. Having spent time working with USA Basketball in recent years, Triano has witnessed first-hand how the bonds developed in summer training sessions translate onto the floor and galvanize team chemistry.
"I think what we do in meetings and off the floor and what we do on the floor is all going to be part of whether we can mesh as a team," Triano said. "We have to use the experience we have from guys who have played in the past and represented Canada and we have to use the young influx of talent and find ways to get them that international experience. No better way then to go one on one every day upstairs in practice."
With more attention on the program and Canadian talent than ever before, Nash stressed the importance of remaining focused on their long-term goals.
"Obviously, we're desperate to qualify," he said of the World Cup. "But the truth is it's going to be a real challenge. We've got a tremendously young team. We have a lot of guys who have very little international experience and very little experience playing together. The challenge is there."
While the FIBA Americas Championship is the first goal, Nash's sights remain set on the bigger picture.
"Our top players are all in," Nash said. "It's a beautiful thing. They're getting a lot of love and interest from people in Canada. This boom of young talent that's entering the NBA and potentially going to the NBA, I believe fans and television viewership is up 19 per cent or something in the past year or two in this country. That, in many ways, is interest in those young players. I think our players are paying back the interest by being all in."
Canadians can get their first look at the squad next week when the team plays host to Jamaica at the Jack Donohue International Classic on Aug. 8 and 10 in Toronto.
Note to readers: This is a corrected story. A previous version said Andrew Wiggins is attending Kentucky.