Welsh First Minister Mark Drakeford says he will back a further referendum if MPs cannot resolve the Brexit deadlock in the next week.
Mr Drakeford said leaving the EU without a deal would have effects that will “be felt by everyone”.
On Tuesday Welsh Government ministers outlined risks on health, the economy, transport and farming.
It comes after Prime Minister Theresa May’s deal to leave the EU was resoundingly rejected by MPs last week.
Much of the assembly’s business on Tuesday was scrapped, making room for statements on Brexit preparations.
Some Brexit planning is being kept under wraps, according to BBC Wales Brexit correspondent James Williams.
The Welsh Government had opposed Mrs May’s deal, and prefers one that binds the UK closer economically to the EU.
Of a no deal Brexit, Mr Drakeford told the Senedd: “The impacts are potentially far ranging, and will be felt by everyone. These are not theoretical or hypothetical concerns, but the reality of where we may now find ourselves.”
“Even at this late hour, Parliament must explore every way of delivering an outcome to the Brexit process that simultaneously respects the referendum and protects us from damage to our economy and the fabric of our society.
“But the debate in Parliament over the next week is the last opportunity to rally around that form of Brexit, one which has at its heart a future relationship based around continued participation in the single market and a customs union.
“If that cannot be done, the severity of ‘no deal’ is so great that if Parliament cannot agree a majority position on a deal that secures our long term economic interests, then the only option which remains is a second public vote to break the deadlock.”
The first minister added: “In 2016 the advice of the Welsh Government was unambiguous; that our future was best secured through continued membership of the EU.
“Nothing in more than two long years of detailed work on Brexit has led us to change that view.”
Mr Drakeford called for Mrs May to take a no-deal Brexit off the table and extend article 50 – the mechanism by which the UK leaves the EU on March 29.
Health secretary Vaughan Gething warned that while the number and type of medicines that might be effected by a no deal Brexit is “relatively low”, “the UK Government cannot provide full assurance that Brexit will not affect business as usual”.
He said he is concerned about “about the future supply of radioisotopes to Wales”, which have no sources in the UK and are imported from other EU countries.
Disruption from customs checks at our ports is likely to render radioisotopes useless for healthcare treatment, he said.
“A no deal Brexit will inevitably lead to a tighter health and social care labour market across the UK,” he said. “That will make it even harder for us to compete for staff and a likely rise in the costs.”
A study has been commissioned by Ipsos Mori “to assess the composition of the social care and childcare workforce in Wales” to find how many EU workers are employed in the sector.
Analysis by James Williams, BBC Wales Brexit correspondent
In the ‘Being First Minister’ documentary that followed Carwyn Jones’ last months in office, there’s a scene in which he’s taken to task by his special advisers for saying in the Assembly that the Welsh Government is not planning for a no-deal Brexit.
Back in November 2017, Mark Drakeford, then effectively the Welsh Government’s Brexit Secretary, told a committee of AMs: “No amount of public money, no amount of preparation, will avoid the harm that will be done to Wales and its economy by leaving the European Union without a deal.”
Having now stepped-up to the top job, Mark Drakeford is trying to give a very different impression of a government that is doing all that it can to prepare for the possibility of a no-deal Brexit – limited as that may be.
But despite the six statements in the assembly on Tuesday, a Welsh Government source tells me that ministers are purposefully keeping some of the no-deal Brexit planning, specifically around emergency planning, out of the public domain for fear that they become self-fulfilling prophecies.
They are, however, keen to get one overarching message out there time and again – a no-deal Brexit should be taken off the table.
Ken Skates, the minister responsible for transport and the economy, said a no deal Brexit could “cause severe disruption to the transport network and connected services within Wales”.
He said there could be delays at ferry ports. While Pembroke Dock and Fishguard have space for delayed vehicles, Holyhead would find it more difficult.
Although UK government modelling says delayed traffic could be dealt with within the port, contingency measures are being considered and the nearby Road King truck stop and other sites have been identified.
Mr Skates said there would be a large impact on food if there was disruption at Dover.
Earlier Gareth Bennett, UKIP group leader, partly welcomed the statements being made by the Welsh Government.
But he questioned why a whole day’s business had been scrapped “largely to indulge in a day of project fear”.
Earlier on Tuesday rural affairs minister Lesley Griffiths told a press briefing she was concerned that only 1,600 farmers had signed up for a red-meat benchmarking scheme to prepare for Brexit.
It was open to 2,000 and offered farmers £1,000 to take part.
She said she had expected the scheme to be oversubscribed.
“I think it is a bit disappointing – I do wonder if farmers have buried their heads in the sand a little bit around Brexit,” she said.
Ms Griffiths, who had met farming unions on Tuesday night and Wednesday morning, said industry leaders had told her that a no-deal Brexit posed a “cliff-edge of a perfect storm of really significant disruption to the Welsh economy”.
She added that the shellfish industry was “really vulnerable to a no-deal”, which she said could lead to the industry collapsing.