The Welsh assembly is heading for a political crisis over its 2007 budget.
The assembly budget must be agreed by AMs by next Wednesday
Opposition parties, which hold a slim majority, had threatened to form a coalition government if the Labour administration does not change plans.
But Labour says defeat on the budget vote would leave public services in limbo, and announced extra money for schools, foster carers and hospices.
First Minister Rhodri Morgan said he will only resign if opposition AMs passed a no-confidence motion in him.
Originally some £14bn was offered by Finance Minister Sue Essex for all public services in Wales, but opposition parties wanted more money for schools and higher education.
At a joint news conference the opposition leaders - whose parties have a majority of one if they all vote together - said Ms Essex should move on their demands for £22m extra for education.
They are asking for £16m for schools and a further £6m for universities which they said would bridge what they claimed was a gap in higher education funding between Wales and England.
Two party leaders, Nick Bourne for the Conservatives and Mike German for the Liberal Democrats, said the opposition would take over in a coalition if they were forced to.
However, Plaid Cymru leader Ieuan Wyn Jones, later said voters were not interested in "tittle tattle" about the assembly and called on Mr Morgan to engage with opposition parties to meet their demands.
The assembly manages a budget of some £14bn
Mr Morgan said the opposition parties "keep changing their tack" on their demands.
Speaking on Radio Wales, he issued an apparent challenge to the opposition parties to say how they would change the budget proposed by Labour and to put down a no-confidence motion in him.
He said: "The big test for any minority government is whether you can get a budget through.
"Clearly, if we can't get a budget through it's up to the other parties who are stopping the budget going through to put a motion of no-confidence down. And they could do that tomorrow.
"All they've got to do is tell the people of Wales where are the savings going to come from.
"Say what you would add and say what you'd subtract to give you the same total. Because the one thing we can't do is increase the total."
Ms Essex earlier said an extra £14.4m from reserves to allocate to public services was a "good balance" between competing demands.
She said: "Clearly, it will never be possible to meet every request and I hope that people will understand that we have to work within the finite resources we have".
Plaid Cymru leader Ieuan Wyn Jones responded by saying the proposed budget would not have to be cut to meet opposition demands to give extra money directly to schools.
He said: "What we have said to the [assembly] government is that we will work with you to find the money within the budget.
"We are offering an alternative. The alternative is for the government to talk to us."
At the opposition parties' press conference, Conservative assembly leader Nick Bourne said the opposition had behaved constructively through negotiations with the government and it was Mr Morgan's duty to "sit down and hammer this out".
Liberal Democrat leader, Mike German, said: "All the balls are in Labour's court."
The vote is due to take place on 13 December.