Naomi Long said it was frustrating for people in the region to be starting another year with further questions about the future of the Assembly.
This week, Northern Ireland First Minister, Paul Givan, said it was “inevitable” that Stormont will collapse if issues around the protocol are not resolved.
Mr Givan said that while he is committed to devolution and wants the Assembly to work, the current situation is not “a tenable position”.
His DUP party leader, Sir Jeffrey Donaldson, has repeatedly threatened to bring down Stormont unless the so-called Irish Sea border is removed.
Reacting to the latest remarks, Alliance Party minister, Mrs Long, told the BBC Talkback programme: “I think it is embarrassing frankly.
“I think most people at home will be frustrated and disgusted that we start into another year with further sabre-rattling about the future of the Assembly.
“This is a critical period, we know that many businesses, many public services, are facing into a crisis with people self-isolating and people ill or off work at the moment.
“We know that our health service has been in crisis and continues to be in crisis over the last number of months and that is likely to be increased as the Omicron variant comes forward.”
Mrs Long said there was much “critical business” that needed to be finished within the current Assembly mandate.
Politicians here need to start weaning themselves off this kind of crisis politics and start focusing on doing the job they were elected to do
She said: “I have two pieces of substantive legislation that are moving rapidly through the Assembly but those would be lost if the Assembly were to collapse.
“There is also legal business which has to be done, such as setting a budget.
“If we don’t do that, then, departments will not have the legal basis on which to continue to spend and invest in public services.
“All of those things require a Government. So if people want to make a point, of course, they can explain why these issues are important, but holding to ransom Northern Ireland’s administration to me is just completely unacceptable.
“Politicians here need to start weaning themselves off this kind of crisis politics and start focusing on doing the job they were elected to do.”
The protocol prevented a hard border on the island of Ireland after Brexit, but introduced new trade barriers in the Irish sea between Northern Ireland and the rest of the UK.
While the EU has given concessions on its operation, notably to ease the flow of medicines, these have not satisfied many who oppose it.
The DUP has said the arrangement is not sustainable because it does not have the support of the unionist community.
Speaking earlier this week, Mr Givan said: “I do want the institutions to be able to keep running, to focus on those issues that matter to everybody.
“But I also accept that for any institution to operate effectively, its foundations need to be right and, at the moment, they’re not.
“That does create real challenges for the sustainability of what we’re trying to do at Stormont, because it requires collective buy-in from everyone in the community. And, at the moment, it doesn’t have that.”