The Lib Dem leader said the prospect of Finance Secretary Derek Mackay securing a deal on his Budget was "not looking good" with just days until a vital Holyrood vote.
The minority administration needs the support of at least one other party and if it fails to get the plans passed could move for an election.
Mr Rennie, who wants the cash mainly for education and mental health services, said he was prepared to push the issue to a snap poll.
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Willie Rennie announced his willingness to take down the SNP government
He said the SNP had to be "much more reasonable than they have been so far" and must deliver "a substantial amount of what we want".
Mr Rennie told the BBC's Sunday Politics Scotland programme: "I'm not fearful of an election, although I do not want one, because I don't think it would be in the interest of the country when we're trying to deal with the big challenges of Brexit and also the many other issues round about the economy and education.
"If we don't get what our voters backed us for in May, then I'm afraid we just have to walk away."
He added: "I'm not going to give up too easily on this, I'm wanting to make sure our voters get what they wanted last May.
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The Lib Dem leader made a demand for £400 million in extra public spending
"I've got that duty just as much as the SNP have got a duty to represent their voters.
If we don't get what our voters backed us for in May, then I'm afraid we just have to walk away
Willie Rennie
"They don't have a majority and they need our support so they're going to have to move."
Tories are opposed to a £79 million tax grab on the middle classes while Labour will not back the SNP unless it rethinks cuts for councils.
Yesterday it emerged Mr Mackay may be edging towards a deal with the Greens on tax hikes and local authority funding.
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Mr Rennie admitted his chances of securing a deal did not look god
Co-convener Patrick Harvie has repeatedly called on Mr Mackay to raise taxes further after using new powers to avoid passing on a Tory giveaway for middle-class earners.
The minister has previously ruled out moving away from the SNP's manifesto commitment to freeze income tax rates, but refused to follow UK Government plans to raise the threshold for the higher rate of income tax.
But according to reports he may consider adjusting the rate for higher earners to secure Green support.
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Sun, July 24, 2016
With over 391 thousand followers on Twitter, First Minister of Scotland, Nicola Sturgeon is a prolific tweeter, here are her best quotes.
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Nicola Sturgeon, Leader of Scottish National Party and First Minister of Scotland
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Dereck Mackay may be more likely to go for a deal with the Greens
Mr Harvie told the Sunday Times: "The ball is in the Scottish Government's court. Whatever is decided we won't abstain."
Meanwhile, local government body Cosla has stepped up its war of words with ministers over funding reductions.
In a briefing paper to MSPs ahead of Thursday's vote it said "misrepresentations" over the deal were confusing and damaging.
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Mr Rennie is not looking for an election though he is not afraid of one
The body insisted the revenue settlement for local government for 2017/18 has fallen by £350 million and said it was "inaccurate" to offset this with cash for schools and social care. The Scottish Government said it has "treated local government very fairly".
A spokeswoman added: "The Scottish Government published a budget for growth and public services, which will deliver increased investment in education, the NHS and protects low-income households from tax hikes.
"The Finance Secretary is currently in active discussions with political parties about the Scottish Budget while considering the detail of propositions received to date and will continue to take forward constructive discussions on Budget plans."
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