The Welsh government will need an opposition politician to help pass its plans in the Senedd, with a final vote planned in March 2025.
It is looking likely the government will have to do a deal with Jane Dodds, the only Welsh Liberal Democrat in the Senedd.
In an interview with Radio Cymru, Dodds did not rule out her involvement.
“It’s important that we get the budget through and we get the money in full,” she said. “I’m open to speaking to them but I don’t know what will happen yet.”
She later said the draft budget was a “missed opportunity” which had failed to deliver on childcare.
Dodds said an extra £20m would only “paper over the cracks”. Despite her criticism, it is understood that talks remain ongoing with the Lib Dem.
A Plaid Cymru politician appeared to rule out a deal on budget on Tuesday morning.
The party’s finance spokesperson Heledd Fychan, asked if she was up for a budget deal on Radio Wales Breakfast, said “No. We want fair funding for Wales.”
Later, she added: “Labour’s budget is underwhelming, unambitious, and falls woefully short of what’s needed to support Wales’ struggling public services.”
In the Senedd, Drakeford said Plaid Cymru faced a “day of reckoning” over whether to vote against the budget.
He said he was open to discussing the spending plans with Plaid but if the party was not interested “the people of Wales will see through you and the political games you think you can play with their futures”.
In response, Plaid leader Rhun ap Iorwerth said: “This is Labour’s budget to pass. They will have to reflect on whether shouting at us in the chamber is the way to achieve that.”