Even though the Liberals included many NDP-friendly measures in the May 2 budget, Horwath has added three more asks to the list, saying she wants more accountability.
"She was quite, I think, open to hearing my concerns," she said after the half-hour meeting in Wynne's office.
"She was open to having me explain to her why it was that it was important for us to take the necessary time to talk to Ontarians about their concerns with the government."
But Horwath wouldn't say whether she'll pull the plug on the minority Liberals and trigger an election.
"That will be determined by the premier's decision," she said. "The ball is in her court now and she has to make that decision and be public about it."
However, Wynne's apology for the $585 million spent to cancel gas plants in Oakville and Mississauga shows she's getting the message that she must be more accountable to the public, Horwath said.
"I think that was an acknowledgment that things can't continue in the same vein as they have had in the past," she added.
A senior Liberal source called it a fruitful discussion, saying Wynne isn't rejecting any of the NDP's demands outright and feels the two can work together.
They may meet again to talk about the budget, the source said.
Before Wednesday's meeting, Wynne expressed confidence that the budget contained all the elements to bring the NDP onside.
The political landscape has "shifted a bit" after the Liberals in British Columbia defied terrible polling numbers to win a majority government Tuesday, she said.
"But I've said all along that I believe that there was enough common ground for us to be able to get a budget passed in Ontario this year, and I think that our budget reflects that possibility," she said. "And so I'm optimistic."
An agreement with the New Democrats is crucial for the Liberals, given that the Progressive Conservatives are pushing for an election.
Horwarth is asking for a financial accountability office, modelled on the parliamentary budget office in Ottawa, and ombudsman oversight of the health-care sector, such as hospitals and nursing homes.
She also wants the Liberals to put the brakes on plans to allow drivers without passengers to pay a toll to use high-occupancy lanes.
But she refused to say whether her party will vote against the budget if the Liberals don't agree to her latest requests.
"I have said that there is no line in the sand," Horwath said.
"We made sure today that the premier was well aware that Ontarians expect better. Not just apologies, but actual behaviour change — a change in direction, a change in the way that they are accountable."
Wynne has been putting pressure on Horwath to make a decision, saying the measures promised in the budget need to be implemented as quickly as possible.
But that isn't expected any time soon, as Horwath still needs to consult with her caucus, who are divided over whether to support the budget.