William Irving, the national teams director for sprint and slalom events for USA Canoe/Kayak, known as Usack, said the organization was chronically underfinanced.

“It’s a Catch-22,” Irving said. “If we had additional funding to apply toward athletes, maybe we could be more internationally competitive. You have athletes that if they had additional funding and support, they could get into more training camps, more funding to purchase more equipment to stay up with other athletes.”

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Rafal Smolen, Usack’s slalom national development and coaching manager, recalled working with a talented young paddler who was forced to face the question of how broke is too broke.

“She had to make a decision to stop training because financially it was too big of a burden to continue,” Smolen said. “It was kind of sad for me to see an athlete that was going up in the progression of the sport and then just had to decide to stop training because she wasn’t able to financially continue with all the expenses.

“It’s hard for her and it’s hard for me. It’s hard to convince a person in that situation to continue. It’s difficult to say, ‘You have potential, you can do it, but you have to figure out how you’re going to pay for it.’ ”

Usack’s annual budget, a combination of United States Olympic Committee contributions and money the organization raises from individual and corporate donors, is less than $1 million, Irving said.

Compare that with the more than $20 million annually Steve Penny has to work with as president of USA Gymnastics, which oversees the American teams in one of the most popular Olympic sports.

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“Our goal is to support any athlete who wants to train full time,” Penny said. “We are fortunate to be in a financial position to do that.”

The amount of money the U.S.O.C. disburses to each sport is based on its predicted medal count and individual performances. In 2011, the committee operated with revenue of $141 million. The sports that are expected to bring in the most medals receive the most money. Eichfeld is bracing for an austere year.

“We didn’t perform very well in London, so we are going to lose a lot of funding,” he said of Usack. “We’ll have a very low staff, one coach for a team of up to 12 athletes, which can be very overwhelming.”

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The fluctuation in financial support takes a toll.

“Without support, you can’t put in the hours to be the best in the world at something; it’s just plain and simple,” Hurd, 26, said. “I don’t think any athlete without a support system of any kind would be able to train at a high enough and a smart enough level to obtain true greatness and compete at a very high and international level. There’s not enough time in the day to spread yourself thin enough to do it all.”

But as soon as it appears that the athletes are spent — exhausted by the continual grind of raising money, working odd jobs and pushing their bodies — they seem to snap back into Olympic mode.

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“I’m very accustomed to having to find my own way,” Eichfeld said. “I usually work two jobs at a time to build funds I need to go wherever I need to go during the summer, so my entire fall, winter and spring is accumulating funds to get where I want to go — and then constantly repeat the cycle. Build up these funds and then I spend them, then I’ve got nothing again, then I build it back up. It’s probably the same exact way for other athletes. It’s what we love, so we make the sacrifices.”

For Hurd, who has worked as an auto mechanic and a blacksmith and is now serving food in the kitchen at a retirement community, it is hard to imagine life without a canoe. His father, like Larimer’s, was a competitive paddler. For a few years, Hurd lived out of the back of a vehicle while chasing his sport across the country. He has now settled in North Carolina with his fiancée, Rebecca Kirlin.

“I love to do it, it’s my career, it’s what I do,” Hurd said. “The money part is hard, and if that’s all I cared about, I’d do something else. Decisions will have to be made, whether to continue on to Rio at this point. We’d love to commit another four years to represent our country in Rio. It’s just, I’m not sure about being in debt for another four years at this point in time.”

In an e-mail, Larimer, 31, Hurd’s paddling partner for two years, expressed similar hopes and worries.

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“Going forward to Rio,” he said, “depends greatly on how much funding me and Eric will receive over the next few years, which is a shame because everyone feels like we could get a lot better with a few more years under our belt.”

So as the million-dollar smiles of American champions — the women’s soccer and gymnastics teams, the female sprinters, the swimmers Ryan Lochte and Phelps —grace billboards, cereal boxes and fast-food advertisements, a legion of others less decorated but no less dedicated prepare for futures in which the only certainty is sacrifice.

“It’s a passion,” Hurd said. “I never really thought about the other side. What am I going to do? It was doing what I needed to do to get by.”