Klinsmann has already met his pre-tournament goal of reaching the last four after helping his side navigate a challenging group phase and an awkward quarter-final against in-form Ecuador.
But despite a raft of suspensions which will decimate his first choice starting line-up at Houston's NRG Stadium, Klinsmann is bullishly talking up his team's chances as they prepare to take on the might of Argentina.
"There's no reason at all why we can't win Copa America," Klinsmann said on Sunday.
"We travelled the world the last few years to very difficult friendly games all over Europe and in Mexico and we came away with wins."
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In Brazil two years ago, Klinsmann's side helped eliminate a Cristiano Ronaldo-led Portugal and highly rated Ghana before qualifying with Germany in the World Cup's "Group of Death."
"Two years ago we had Mr Ronaldo against us in Manaus. And we led them 2-1 until the 96th minute," Klinsmann said of his team's first round World Cup match, which finished in a 2-2 draw.
"We surprised a lot of people -- no one gave us a chance to get out of the group in Brazil. We left Portugal behind, we left Ghana behind.
"Anything is possible in knockout games. You're 50-50 with whoever you play against," he said. "Dream big -- why not? This is about two more games."
Although Klinsmann has urged his team to shed their underdog mentality, insisting he wants them to be bold against more heralded opponents, a gung-ho approach against Argentina could be disastrous.
When the relentless US pressing dropped off in the second half against Ecuador in the quarter-finals, the South Americans created chance after chance only to be let down by poor finishing. Argentina, who have amassed 14 goals in four games, are unlikely to be as profligate.
"We're on the right track, but it will be very difficult playing in front of the American crowd. Physically they are a very strong team and they can do a lot of damage if they are allowed to play," warned Messi.
Yet it is hard to see anything other than an Argentina victory which would leave Gerardo Martino's side 90 minutes away from ending a 23-year wait for a major title.
"It is clear that I want to win something with my country and I want to do everything I can to make that happen," said the Barcelona superstar.