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Executive parties have been in negotiations with the government in a bid to get increased funding.
While the government's offer has not changed, Sir Chris spoke to executive parties on Thursday afternoon.
He is expecting to hear back from them next week as to whether they will accept what is on the table.
"I cannot emphasise enough how tight the financial situation is and the pressure on the public finances," Bryant said.
He said the £1.5bn "gives the executive the chance to manage its immediate pressures, and move towards a more sustainable footing".
"Not just this, it supports them in delivering much-needed transformation of public services, and to invest in social housing," he added.
He urged politicians to get together and work out a balanced budget as a "matter of urgency based on these figures".
Sir Chris added that this "requires the executive to recognise the financial landscape across the UK , and do its bit, to find efficiencies and to raise additional revenue".
However Finance Minister John O'Dowd previously said the current published financial pressures facing Stormont departments were around £1.6bn, adding: "So we have a bit to go."
A Sinn Féin spokesperson said the "current offer from the British government falls well short of what is required to fund, transform and improve our public services".
"The north receives less in funding than Wales and Scotland which if addressed would give us a transformative increase of between £1 billion and £3 billion.
"People here pay their taxes and have the right to properly funded public services and our public service workers deserve proper pay settlements."
It is not clear what will happen if the executive refuses to accept the offer from the government.
Sir Chris could seek to pass a budget bill for the executive via Westminster, but this would prove a contentious move in a period of devolution.
The offer on the table from the government includes £450m extra for day-to-day pressures this year, as well as an additional £400m in 2027/28 and 2028/29.
