Sinn Féin's Martin McGuinness was speaking ahead of Saturday's meeting by his party's ard chomhairle (national executive) to discuss the crisis.
He said he was told the UK government plans to impose £12bn in welfare cuts.
He said Tory ministers plan a further £13bn in cuts across UK government departments.
The issue of welfare reform and its impact on Northern Ireland's budget has caused serious political difficulties at Stormont in recent years.
The crisis deepened earlier this week when the Welfare Bill was blocked by Sinn Féin, the SDLP and the Green Party's only MLA.
The welfare legislation was an important part of last December's Stormont House Agreement, and would have provided a number of mitigation measures to protect people on benefits who may otherwise lose out under planned welfare changes.
Some of the reforms are already in force in other parts of the UK, but speaking ahead of this party's meeting in Dublin, Mr McGuinness said Northern Ireland was different from the rest of the UK.
"I am not prepared to reside over the austerity agenda that the British government are inflicting on our executive. My conscience would not allow me to do it.
"So I think what we have to do is rally the forces, both in Dublin, in the United State of America, and make it clear to David Cameron that this approach is folly of the worst kind," he said.
But First Minister Peter Robinson, who leads the Democratic Unionist Party (DUP), said there would be no renegotiation of the Stormont House Agreement.
He warned that failing to implement welfare reform would result in "£600m of cuts to vital public services".
Mr Robinson was interviewed at the Irish Open golf tournament, during his first public appearance since suffering heart attack last Monday.
"I've had the experience of being in hospital, talking to medical staff, knowing the difficulties that they're facing, the fact that without the funds that they presently have there would be loss of life, it would be an issue for public safety," Mr Robinson said.
"So, we do have to deal with all of these issues, but if they can't be dealt with then Her Majesty's government is going to have to step in and deal with them themselves."
On Wednesday, Northern Ireland Secretary of State Theresa Villiers said she could not rule out Westminster having to step in to legislate on welfare matters in Northern Ireland.

Sixty-two-year-old Gillian Sandle, was a passenger in the vehicle which was travelling through Havant, near Portsmouth, on Sunday lunchtime.
Members of the public tried to revive her, but she died in hospital.
Ms Sandle's family said they were "totally devastated at the sudden and tragic loss of such a wonderful lady".
Police are appealing for witnesses to the accident in North Street between 12:35 and 12:40 GMT.
The vehicle was a blue Volkswagen beach buggy.
Sgt Melanie Adcock of Hampshire Constabulary said: "This incident took place at a busy time of day when there were lots of Christmas shoppers in North Street so it is likely many people saw what happened.
"I would like to hear from anyone who witnessed any part of this incident."

The company posted net income of $4.9bn (Â£3.4bn) for the fourth quarter, an increase from $4.7bn a year ago.
The announcement sent its share price up 9% in after-hours trading.
That means that Alphabet is now worth around $568bn, compared with Apple which has a value of $535bn.
It is the first time that Alphabet has stripped out the results of its Google business - which includes the search engine and YouTube - from its "Other Bets" business, which includes more experimental ventures such as self-driving cars and internet balloon programs.
The figures show that the "Other Bets" lost $3.6bn in 2015.
But advertising revenue for Google rose by 17% to $19.1bn, in the three months to December as the number of ads, or paid clicks, rose.
Alphabet's claiming of the most value company title has been seen by some as a passing of the technology baton. Google apps and devices compete for market share against Apple iPhones.
The title of most value company in the US has been passed between technology companies for several decades.
Apple became the United States' most valuable company in 2010, when it dislodged Microsoft. Microsoft in turn overtook IBM two decades earlier.
Northern Ireland's deputy first minister has described the political situation at Stormont as "very grave" due to the row over welfare reform.
[NEXT_CONCEPT]
A woman was killed when her scarf got caught in the wheel of a beach buggy she was travelling in.
[NEXT_CONCEPT]
Alphabet- Google's parent company- has surpassed Apple as the world's most valuable company after its latest earnings report.