The INMO says Leo Varadkar faces a difficult job as Minister for Health.
He took over from Dr James Reilly in the cabinet reshuffle yesterday.
"There's no quick fix for health," said Deputy General Secretary of the INMO, Dave Hughes.
"It's with us all the time - the needs are growing, the population is growing, and the staff numbers are dropping. It's a very, very difficult ministry he's taking on board."
Meanwhile, Trevor Duffy, President of the IMO, said that staffing will be one of the huge obstacles that Leo Varadkar will face, as qualified doctors and nurses are leaving Ireland for better opportunities abroad "at an alarming rate".
He did, however, say he was confident about Varadkar's appointment.
"It's a relatively shot period of time he'll be in this position for … but I think he's shown himself to be fairly productive in his last role, so I'd be fairly hopeful."
For his part, Varadkar remained optimistic about the task ahead of him.
"We're a country that spends pretty much as much on health, per capita, as other European countries, but we definitely do not have a European-standard health service," he said.
Leo also had a word to say about one of the Department's nicknames.
"I do know another thing people call the Department of Health is 'Angola'. But I do note that Angola is one of the fastest-growing and booming economies in Africa.
"So if you can turn Angola around, I'm sure someone can turn around health."
Varadkar identified the consistent budget over-run as one of his main priorities - saying that while there were only a few months remaining in this fiscal year, he intended to being the department in line after the next budget.