The secretary of state is in Northern Ireland for meetings with executive parties about the budget deadlock.
Sir Chris Bryant, who has insisted there is no more money available beyond the £1.5bn the government has already offered, has accused executive ministers of being financially "irresponsible".
Having held brief virtual discussions with parties last Friday, Sir Chris met leaders of the four executive parties separately at Stormont on Thursday.
The executive has maintained it cannot balance its books without more support from London.
The current package would be split into three tranches with £525m available this year, but the Stormont parties said that still falls short of what they require.
Without an agreed budget, public sector workers in Northern Ireland cannot receive long-awaited pay awards that they are entitled to, in line with their counterparts in other parts of the UK.
Last month, Sir Chris made an offer of a financial package worth about £1.5bn over the next three years.
But executive parties said that did not go far enough and they have argued that significant gaps remain before they can agree to a deal that would allow them to set a budget.
On Wednesday, the secretary of state told the House of Commons there had to be "political accountability for finances", and that he wanted to be able to settle the issue with the executive.
The government is due to publish its own budget next week, with Prime Minister Andy Burnham previously saying the executive needed to be "realistic" about what more Westminster could do, given some Whitehall departments are being asked to make in-year cuts.
Following talks on Thursday, Sinn Féin leader Mary Lou McDonald accused the government of "attempting to shortchange" people in Northern Ireland.
She said extra funding offered to the Stormont executive "falls well short" of what is needed to deliver public services and staff pay deals.
McDonald said the government "needs to come up with the right resource to ensure that society and communities don't suffer".
"They can't short change people who live here. We won't accept, or sign on or tolerate that," she told reporters at Stormont.
McDonald added: "I believe on this point, if on little else, there is agreement right across the executive and the political spectrum here, that the British government is attempting to shortchange the north of Ireland - and that we will collectively face that down."
Democratic Unionist Party (DUP) leader Gavin Robinson described talks with the secretary of state as "uncharacteristically" constructive.
He said their discussions now had a "sense of realism" and provide an opportunity for the executive to have a "fighting chance to balance the books".
"I think it is now clear to the secretary of state that no matter whether this executive passes a budget or indeed he steps in and government pass it on the executive's behalf, the books cannot balance," he said.
The DUP leader said his party and the Northern Ireland secretary remain "in different places", but there was "a good starting point now from where we can attempt to get to a place that would be of a better import for our public and public services".
"I do think there is an opportunity for us to continue engagement and also look toward Wednesday of next week to see whether the gap can be closed sufficiently that would allow the executive a fighting chance to balance the books."
Robinson said it "wouldn't be realistic to imagine that the gap will be entirely closed" in Stormont's budget pressures.
"But I do think that when we consider the discussions we've had, the money on offer, the ability to reprofile some other monies that rest at the executive's disposal but have constraints around them, and also what will come next week, it'll take us a huge step forward," he added.
The DUP leader said he believed that "when the gap is smaller, when it is more manageable and there is realism at the heart of these discussions, then we could progress positively".
Hospital doctors have announced they will strike next month over the issue, while the Royal College of Nursing is also balloting for industrial action.
At Stormont's finance committee on Wednesday, the Department of Finance's top civil servant Neil Gibson confirmed that it is now too late for any civil service pay settlement before Christmas because of the ongoing lack of a budget.
"We're too late in the year for Christmas for the sector I'm in," he told assembly members.
Sir Chris has suggested the absolute deadline for reaching a deal is January because at that point the money available to departments to spend under emergency arrangements will run out.
Stormont departments are facing a shortfall of up to £1.6bn, according to a spending watchdog.
With no agreed budget, public services have been operating under contingency arrangements allowing departments to spend up to 95% of last year's funding.
