The Scottish Liberal Democrat leader said his party was prepared to push the issue to an election if its priorities were not met by Finance Secretary Derek Mackay.
Mr Mackay needs to win support from at least one of the other Holyrood parties to get the minority SNP administration’s tax and spending plans through the Scottish Parliament.
A draft budget bill has been published in advance of MSPs voting on its general principles on Thursday after an earlier parliamentary debate ended in stalemate.
As part of the negotiations, the Liberal Democrats are seeking £400 million of extra cash for priorities including education and mental health while the Scottish Greens have said their support is contingent on changes to bring in “progressive taxation”.
Mr Rennie told the BBC’s Sunday Politics Scotland programme that while constructive talks had taken place with Mr Mackay, he believed the gap between the two parties was growing wider.
Asked whether he would countenance a snap election if the Government cannot get plans through Holyrood, he said: “I’ve floated that prospect this week because I believe it is not looking good for an agreement this week and, if anything, the reaction I’m getting from people on the doorsteps and people contacting me through email and other means, they are saying ‘well, yes we should have an election’ because they would like to get rid of this SNP government.
“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.”
Mr Rennie called on the SNP to be “much more reasonable than they have been so far” and insisted he was willing to push the issue to an election unless they delivered “a substantial amount of what we want”.
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.
“I’ve got that duty just as much as the SNP have got a duty to represent their voters. They don’t have a majority and they need our support so they’re going to have to move.”
The Scottish Conservatives have said the budget would “act as a ball and chain on growth”, publishing analysis suggesting that had Scottish growth matched UK figures since 2007, gross domestic product would have been £3.1 billion higher over the last ten years.
Scottish Labour leader Kezia Dugdale has written to Finance Secretary Derek Mackay arguing that the plans will cut hundreds of millions of pounds from local services.
A Scottish Government spokesman said: “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.”