They haven't played a home tie for three years. They don't have a sponsor, and for a long time, their national federation wasn't recognised by their own government.
And ahead of their clash with New Zealand, team captain Maurice Ruah had to pay for all their flights to Auckland with his own credit card.
There may be sports here that have issues, but spare a thought for those involved in Venezuelan tennis.
To say they face uphill battles is an understatement, since the massive economic and political instability in the country over the past two decades.
Once a relatively prosperous country in South America, due to its large oil reserves and other natural resources, the country has been in a severe economic recession for most of this century, particularly since 2013. Last year, the United Nations assessed that 90 per cent of Venezuelans were living in poverty. There are extremely high rates of unemployment, hyper-inflation and constant food shortages.
"It's really hard," Ruah told the Herald . "The average salary is very low, so people don't have the power of purchase. There's a lot of poverty, they've been through a lot of tough times. A lot of people are even eating out of the garbage.
"We hope things will change and eventually we get a stable currency. We had a terrible devaluation, where you would buy something in the morning, and by the afternoon, if you sell it, you lost money. Re-buying the goods was more expensive than selling; nobody wanted to sell, so a lot of stuff was kept in warehouses and medications was hard to find."
The regime of president Nicolas Maduro since 2013 has been characterised by corruption, massive social unrest and protests and has sent the country backwards at an astonishing rate.
Tennis seems almost trivial in the circumstances, but the sport has been badly affected. They haven't played Davis Cup at home for three years, instead moving to a neutral base in Miami. But this clash with New Zealand was transferred to Auckland by the International Tennis Federation, after Venezuela couldn't afford the costs of hosting the tie.
Their problems have been compounded by politics; for a period, the tennis federation wasn't recognised by the government, and wasn't allowed to have a bank account. And they aren't permitted to open a bank facility in the United States, due to Venezuela government policy.
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That's made it almost impossible to access funding from the ITF, which since they lost their sponsors is their sole source of finances. The ITF covers 90 per cent of the expenses for Davis Cup ties but those payments have been frozen.
Ruah paid for all the expenses relating to their tie with Ecuador last September (food, stringing, transport, courts) and is still waiting to be reimbursed, as the ITF struggle to find a way to facilitate the transfer.
"We cannot open a bank account in the United States," explained Ruah. "And there is no way you can send dollars to Venezuela. It's difficult, a very special situation. It's been almost six months since we played the last Davis Cup, and we were hoping to get some of that money to fund this event in Miami. But it didn't happen."
Ruah, who reached a career high ATP singles ranking of 90 in 1994, has lived in the US for 20 years, one of around three million Venezuelans (about 10 per cent of the population) who have emigrated. He remains a tennis fanatic, and at 49 years old is listed as their fourth playeer for this tie ("but only if something happens").
● New Zealand and Venezuela are level at 1-1 after the opening day's singles rubbers in the Davis Cup tie in Auckland. Venezuelan No 2 Luis David Martinez beat Ajeet Rai 5-7, 6-4, 6-2 in the second singles rubber after Finn Tearney defeated Jordi Munoz 6-4, 6-4 in the opening match.
Today's doubles now has added importance, with New Zealand featuring ATP pros Marcus Daniell and Artem Sitak the overwhelming favourites against Munoz and Martinez.