The threat of industrial action comes after IAG - the company formed by merging BA and Iberia - revealed an operating profit of just £13.5m in the nine months to September 30.
In addition to cutting nearly a quarter of the workforce, IAG has proposed a staff salary cut of 25-35% for three years.
"We are willing to take any necessary action," the airline unions said in a statement.
The results show Iberia is the weak link in the group, making a standalone operating loss of £209m in the period, while BA contributed operating profits of £228m.
On a pre-tax basis, taking wider cost pressures into account, the group made a loss of £134m in the nine months.
IAG shares have shed 40% of their value since the group's formation in 2011.
Iberia is Europe (Chicago Options: ^REURUSD - news) 's leading carrier to Latin America, but it has been battling against increased competition from low-cost airlines and high-speed trains, labour disputes and Spain's deep economic crisis.
It is bleeding cash as revenues fail to cover its high operating costs, with a 15% spike in fuel costs.
"Iberia is in a fight for survival and we will transform it to reduce its cost base so it can grow profitably in the future," IAG chief executive Willie Walsh said in a statement.
Mr Walsh is no stranger to battles with trade unions and took on employees of BA over reforms when he was boss of the UK flag carrier.
He has also been a vocal critic of the British Government's aviation policy and said it was a "disgrace".
A BA cabin crew strike in 2010 cost the airline up to £7m per day.
Mr Walsh stood firm on an airline's decision to withdraw travel perks from striking cabin crew, but staff called the ploy "bullying tactics".
Mr Walsh rejected suggestions the withdrawal of concessions was a "punishment" or an attempt to "break the union".
He added: "We told them about the consequences if they went on strike."
IAG's transformation plan for Iberia includes the fleet being downsized by 25 aircraft and routes cut by 15% in 2013, to concentrate on longer haul, profitable destinations.
Iberia head Rafael Sanchez-Lozano said: "It is unprofitable in all its markets. We have to take tough decisions now to save the company and return it to profitability.
"Unless we take radical action to introduce permanent structural change the future for the airline is bleak."
Whilst the possibility of strikes by Iberia staff now loom, passengers booked from Heathrow to Madrid should feel secure, Business Travel News editor-in-chief Malcolm Ginsberg.
"From a practical point of view if an Iberia flight is cancelled at short notice it should be relatively easy to transfer to British Airways - providing they have space."
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