They claim that if their funding does not improve courses could be cut, jobs could go and research work might not happen.
They argue public funding from the Scottish Funding Council has fallen by 12% in real terms since 2010.
Universities get their money from a wide range of sources.
The Scottish government, which finances the Scottish Funding Council, argues it has invested Â£4bn in higher education over the past few years and is investing more than Â£1bn this year. Political critics claim it is underfunding universities.
The warning came in evidence to MSPs on Holyrood's public audit committee on Thursday.
Alastair Sim of Universities Scotland said: "We welcome the Scottish government's close engagement with the sector in recent months to try and find a way through these funding challenges together.
"The government has reiterated its commitment to an excellent, competitive and accessible higher education sector. We recognise the pressures facing the Scottish budget this year and have offered a range of creative ways to make investment go further.
"However, universities do need to see an end to the erosion of public funding for teaching and research in this year's budget as the first step to recovering a sustainable position. They simply cannot absorb any more cuts. We look to the December budget with confidence."
The question here is whether universities receive enough money, could attract more or are always run as efficiently as they could be.
The debate some in the sector want is a complex one - it is not a simple appeal for more cash from the government. Indeed solving the financial problems facing the sector is not straightforward.
The current Scottish government is committed to maintaining free tuition for undergraduates and this policy is not in doubt - universities in Scotland support it.
As with any business, the biggest single cost for universities is staff wages.
Universities get their income from a number of sources including:
The proportions vary from university to university. Most courses will have students from Scotland and the rest of the UK - many, especially at the older universities, will also have students from outside the EU.
Naturally, the issue of free tuition for Scottish students is likely to attract the greatest public interest.
Universities Scotland claims the money from the Scottish government to cover free tuition is not enough to cover the overall cost. The implication is that these free places are being partly subsidised by the other money universities receive.
A report from the spending watchdog Audit Scotland report found that universities recovered 94% of the full economic cost of teaching publicly-funded students in 2014/15.
This has since fallen to 90%, according to an analysis by Universities Scotland of the Audit Scotland data.
Some universities though are in deficit overall. Gaining extra income is a challenge.
Significantly increasing the income from students from outside Scotland and the EU could be difficult. There are vital questions over how many more students they could attract and find places for.
The decision to leave the EU also poses a challenge to university research funding. Some fear research funding from EU-wide funding bodies will be lost. They hope the UK government will agree to keep contributing to the EU funding bodies after Brexit.
The concern is that financial problems will lead to job losses and courses being cut. But because universities are independent institutions which get their money from so many different sources, simply drawing a straight line between any cuts, their overall financial situation and the amount they receive from the government is not straightforward.
Although the current government would completely rule out charging students for their tuition, it could be argued that tuition fees for Scottish students could allow universities more financial flexibility.
Last year Aberdeen University announced 150 job losses, blaming cuts to research funding. Further cuts came this autumn.
The decision to leave the EU also poses a challenge to university funding. Some fear research funding from EU-wide funding bodies will be lost. They hope the UK government will agree to keep contributing to the EU funding bodies after Brexit.
Despite the financial challenges facing Scottish universities, they have maintained their international standing in recent years - despite fears that free tuition would lead to a funding gap with the rest of the UK and cause a brain drain of the best academics and research staff.
The questions and challenges here are complex, inter-related ones.
Universities are warning that current funding levels are "unsustainable".