The meeting could be crucial for the minority Liberals, who need the New Democrats onside to pass the budget and avoid an election.
The Liberals addressed a long list of NDP demands in the May 2 budget, but Horwath says she wants more accountability.
She's asked for a financial accountability office, modelled on the parliamentary budget office in Ottawa.
She also wants Ontario's ombudsman oversight of the health-care sector, such as hospitals and nursing homes.
Horwath's third demand is to put the brakes on plans to allow drivers without passengers to pay a toll to use high-occupancy lanes.
She won't say whether her party will support the budget if the Liberals don't agree to her requests, but says she hasn't drawn a line in the sand yet.
Wynne has said Horwath's extra demands are "a little surprising," given how many of her requests were incorporated in the budget, such as a cut in auto insurance rates.
The premier is also putting pressure on Horwath to make a decision, saying the measures promised in the budget need to be implemented now.
The Progressive Conservatives are pushing for an election. But they won't say whether they'd give the ombudsman the same powers if they form the next government and have rejected the idea of a financial accountability office.