The Chief Executive of Cardiff and Vale University Health Board told AMs that the health board had a funding gap of £37.5m up to September 2012.
According to the Board's Finance Director Kevin Orford, the total loss for this financial year will be around £25m-£27m after expenditure cuts have been made.
They were giving evidence to the Public Accounts Committee on 4 December 2012.
"The Wales Audit Office rightly criticised our position, but we are determined to get into a balanced position," accepted chief executive Adam Cairns.
He also revealed that preliminary talks between the health board and the government have taken place on the matter.
Committee Chair Darren Millar asked whether the fact that the government has "put its hand in its pockets" in the past to financially assist health boards meant that they assume that this money can be relied on again in future.
"The government has a contingency fund of £50m - the debt for only two health boards, yours and Betsi Cadwaladr, could be £61m," warned Mr Millar.
Former Chief Executive of Betsi Cadwaladr Health Board had earlier stated that he expected to see the health board making a loss of around £19m.
In response to a question from Islwyn AM Gwyn Price about the reasons for their being behind with their financial plans, Mr Lang admitted: "Some of our plans were slow being implemented."
"Some of the savings weren't realisable."
Betsi Cadwaladr University Health Board Chief Executive Mary Burrows said it was "likely" that they would have to borrow money from next year's budget.
"If we have to borrow money from next year's budget, we'll do so with a heavy heart," she added.
There were already concerns that local health boards would not break even this year following the Wales Audit Office's
that they could make a loss of up to £130m for the financial year.
They expect to see a loss of £70m but have also said that the loss could be £46m at best if the health boards find ways to make savings before April.
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