The president of the Teachers' Union of Ireland (TUI) has said the union is working to coordinate with others on any potential strike action.
It comes amid a revised vaccination rollout based on age and not profession.
Martin Marjoram told Breakfast Briefing his members were given assurances by the Government.
"We've been very disappointed as you know, angry in fact, at the sudden reversal in the vaccine allocation plan.
"We had been given assurances that frontline education staff - particularly in second level schools - would be in the first one-third of those who would be vaccinated.
"So the sudden reversal of that, we found out about it frankly through leaks and through angry e-mails and texts from members.
"So even the manner in which we found out about it was extremely disappointing."
He said members will discuss this issue on Wednesday morning.
"We have made time at our congress tomorrow morning to discuss that, to give members an opportunity to establish policy.
"We're trying to coordinate with the other teacher unions in that regard as well".
But Mr Marjoram said teachers had not sought to be ahead of anyone else on the vaccination priority list.
"We never sought to bump anybody off any list - we took the plan as it originally was.
"We could see the clear imperative to prioritise those who are most vulnerable to serious illness and those in healthcare settings; we didn't argue with that.
"Clearly not everybody who's been vaccinated so far has been in a frontline position".
'Not everybody could be vaccinated by September'
And he added that the vaccination programme itself could disrupt schooling.
"It's also worth saying that even though we've a relatively short time left in this academic year, the way things stand now we may well not have everybody vaccinated in time for September.
"So there may be interruptions to schooling - there might be teachers out sick, there may be teachers who have to be given time off to get vaccinated.
"That could interrupt schooling in September.
"We genuinely think that there's every possibility of running the age-based system in parallel with something that is specifically directed towards particular professions", he said.
On potential strike action, he said: "We're not rushing into anything, we obviously want an engagement on this.
"We want to fully understand what the old schedule would have looked like, compared to this new schedule.
"Where exactly we are going to be, for instance, come next August - is there going to be any provision for those who are in more exposed settings depending on what school they're in?
"So we've a lot of water to go under bridges before we get to decisions and ballots".
On Monday, general-secretary of the TUI, Michael Gillespie, told Newstalk Breakfast any move towards strike action is up to its members.
"We expect there to be emergency motions about this issue that arose long after we'd finished the agenda.
"It only occurred last Tuesday where teachers who thought they were being prioritised in terms of essential workers - they weren't expecting to be ahead of anybody.
"They were at number 11 after the Guards, who were at number 10, and they were expecting - like what's happening in other jurisdictions - to be vaccinated parallel to the main body rollout because they are essential workers".
Mr Gillespie added that the re-opening of all schools on April 12th will see teachers working in the most crowded classrooms in Europe.
"Teachers will be in classrooms, crowded classrooms - the most crowded classrooms in Europe, still - where the children won't be vaccinated and can't be vaccinated because there's no safe vaccine as yet for under-18s.
"If a teacher gets COVID, a teacher's out for 14 days... in a post-primary school that interrupts education for two weeks for people.
"The problem is that - because of previous Government [sic] - we have a scarcity of teachers, there's a recruitment and retention problem, so we don't have substitutes to replace those teachers.
"Teachers were not expecting to be vaccinated by the 12th of April, but at least they thought they knew where they were on a list - even though they didn't even know the time of it - now they're not on the list at all".