The government announced the planned redevelopment would either need to be cut back or done in stages, due to a budget blow-out.
A report commissioned by the government found the current plans could not be delivered within the current $1.88 billion budget.
Infrastructure Minister Chris Bishop said it would cost "several hundred million dollars" more than that - possibly up to $3b. And that did not cover costs for things that had not been included: a pathology lab, refurbishment of the existing site and car parking, he said
Invercargill Mayor Nobby Clark said the proposed budget overspend cuts to the Dunedin Hospital project would impact more than just the people of Dunedin and Otago.
"The Dunedin Hospital provides a vital lifeline to everyone across the Otago and Southland regions. On any given day it's estimated that up to a quarter or so of all patients in the hospital come from Invercargill, Southland and Waitaki, so it's imperative that we show our support against the proposed budget cuts.
"I'm sure many of us will have friends or family members who have travelled to Dunedin for surgery or other medical issues. I, myself, spent time in Dunedin Hospital after undergoing heart surgery at the start of the year, so understand how essential these services are to our city."
The council will support and promote the campaign through a number of activities and initiatives aimed at encouraging the public to sign the 'They Save, We Pay' online petition and make submissions to the government.
The 'Invercargill Pays, Too' tagline would be used locally to show solidarity in the campaign.
"Ultimately the people of Invercargill will pay the price for these cuts and we'd urge the government to save people rather than pennies," Clark said.