Two department heads told Treasury secretary Tony Farrell two months ago they would struggle to meet a time frame given to them to identify agency savings for this year's budget.
A Right to Informaton document released by Labor on Friday have shown Mr Farrell wrote to department heads on June 25 with figures the government had decided would need to be cut from each agency and to request a savings plan.
The government wants $450 million to be cut across all state agencies over the next four years.
It has pledged to protect frontline services and wants expenditure on consultants, travel and advertising reduced.
The government wants vacancy control and natural employee attrition to be targeted.
Former Health Department secretary Mike Pervan and Communities Tasmania secretary Ginna Webster both told Mr Farrell by email the seven days they were given to outline savings was insufficient.
Ms Webster said the department had key senior executives on leave at the time and a relevant government minister.
"As a new agency (with critical frontline service delivery operations) the savings ask is significant," she said.
"I do need the time to carefully consider the definition of frontline services and test this with the ministers."
Her request for an extension to June 23 was denied.
Mr Pervan said the department would struggle to produce a "robust" savings plan.
Mr Farrell told the pair he was not in a position to agree to time extensions.
"Whilst the time between the Treasury letter and the time for submission is short, the requirement to produce a savings plan has been known for some time," he said.
"I expect that all agencies would have already undertaken significant analysis and work in this regard."
"The government has committed to publishing savings strategies at the end of the first quarter and also to reporting against those strategies at mid-year."
Labor finance spokesman David O'Byrne said Premier Will Hodgman had known since June what would need to be cut from each department and now needed to detail the quantum of the cuts.
Labor leader Rebecca White said that Ms Webster needed a refined definition of frontline services showed services to Tasmanians would be impacted.
A government spokesperson said:
Tasmanians expect their government to be responsible, efficient and to spend taxpayers' money wisely, which is why there has been ongoing discussions with department heads since the budget was delivered.
Mr Pervan and Ms Webster have since moved on from the departments they led at the time of the email correspondence.