Arlene Foster was speaking after a meeting of the executive on Thursday afternoon.
She told the BBC there were no solutions on the table.
The Stormont parties failed to pass the Welfare Reform Bill on Tuesday.
Mrs Foster said failure to pass the legislation meant that there was a £600m hole in her budget.
She said she cannot move the budget bill required to give Stormont officials the legal authority to carry on spending money after the end of July.
The minister said she is seeking a meeting with the Treasury in London early next week to assess her options.
Sinn Féin's John O'Dowd said Stormont ministers should present a united front and seek a joint meeting with Prime Minister David Cameron.
However, both the Alliance Party and Ulster Unionist ministers said they were pessimistic about the chances of a resolution to the executive's difficulties.

Every practising nurse and midwife must be on the UK register, but not everyone on the register will be practising, or working in the NHS.
However, the government has said that there has been a 13,100 rise in the number of nurses actually working on NHS wards in England since May 2010, when the Conservatives came into power as part of the coalition government.
But this is only true if you look just at nurses working on acute, elderly or general wards.
If you look at all areas of nursing, the number of staff - or the equivalent in terms of full-time hours - did increase between May 2010 and March 2017, the latest date we have figures for, but by a more modest 5,000.
To confuse things further, the Health Secretary, Jeremy Hunt, tweeted earlier this month that there were 15,000 more nurses since he took up the post, in September 2012.
This is because the overall number of nurses working for the NHS in England fell by almost 10,000 between 2010 and 2012 and then went back up again by just under 15,000 between 2012 and 2017, resulting in that net increase of almost 5,000.
This figure includes health visitors, who are qualified nurses.
The overall increase in numbers of nurses working in the NHS masks a net fall in some areas of nursing.
For example, since May 2010, the numbers of community, mental health nurses and specialist learning disability nurses have fallen.
And, meanwhile, the number of nursing posts lying vacant doubled between 2013 and 2016, from 20,000 to 40,000, according to figures from the Royal College of Nursing.
So the gap between how many nurses we have and how many we need has widened.

French Europe Minister Harlem Desir called the move "scandalous" and said it raised questions about the EU's conflict of interest rules.
Ex-commissioners are free to take up a new role 18 months after leaving.
Despite accepting the job after 20 months, Mr Barroso has come under fire for ignoring the spirit of the rules.
Mr Desir drew attention to the ill-timing of the job with Goldman Sachs.
"It's a mistake on the part of Mr Barroso and the worst disservice that a former Commission president could do to the European project at a moment in history when it needs to be supported and strengthened," he told the French parliament, referring to Europe's shock after Britain voted to leave the EU on 23 June.
The bank hired Mr Barroso as an adviser and non-executive chairman of its international business, with a brief of advising the bank on the consequences of Brexit.
Mr Barroso has said he hopes to bring his EU experience to bear as the bank's London operation deals with Britain's imminent negotiation of withdrawal from the EU.
In his new role, Mr Barroso will be able to draw on his intimate knowledge of the EU and have access to many officials and politicians he worked with at the European Commission.
Mr Desir's attack in the French parliament was the latest in a sustained tirade against Mr Barroso's appointment, with some calling it "shameful".
French Finance Minister Michel Sapin told reporters on Tuesday "If you have loved Europe, you shouldn't do this to it, especially not now," adding: "But this doesn't surprise me from Mr Barroso."
The European Ombudsman has called for the EU to tighten rules on commissioners taking appointments after leaving office.
Ombudsman Emily O'Reilly said adhering to technical rules did not absolve former staff of a wider duty to show integrity.
"Any suggestion that the spirit of the law is being ignored risks undermining public trust in the EU," he said.
The finance minister has said she cannot move the budget bill forward because of the inability of the Stormont parties to resolve the deadlock over welfare reform.
[NEXT_CONCEPT]
The number of registered nurses and midwives is shrinking, according to figures from regulator the Nursing and Midwifery Council (NMC).
[NEXT_CONCEPT]
France has called on the former head of the European Commission, Jose Manuel Barroso, not to take up a job advising US bank Goldman Sachs on Brexit.