Republicans at the time said it was just too large and would deliver too big a property tax hit in a sluggish economy.
"I never give up on something I believe in," Corroon, who leaves office in January, told the council. "And this is my last opportunity."
The mayor's calculated cuts seemed to be just enough to swing the Republicans.
"I've wrestled with this," said Councilman Steve DeBry, a Republican. "I want to thank Mayor Corroon for paring this down."
But DeBry was adamant that the language on the ballot be specific as to what voters are getting. "Then let the people decide if they want to raise their taxes," he said.
If approved, a 20-year bond would cost the owner of an average Salt Lake County house $6 per year in extra taxes, according to Corroon's analysis. A $500,000 business would see its tax bill increase $22.
The proposal would allocate $9.5 million for work on the Parleys Trail; $5.5 million for acquisition of park property in Magna; $5 million for development of the Lodestone Park near Kearns; $10 million for a regional park in the southwest quadrant of the county; $6 million for Wheadon Park in the southeast planning area; and $11.5 million for Jordan River Trail.
If approved, the bond would complete almost all of Parleys Trail and the Jordan River Trail.
Council Chairman David Wilde voted to put the bond before voters but said he had "strong reservations" about doing so.
He cited deferred maintenance on county infrastructure and declining revenues in the down economy.
"We can't look at these things in a vacuum," he said. "It's six bucks for taxpayers. But that's added on to new taxes in their cities. Taxpayers get overburdened."
Some 25 Salt Lake County parks and facilities included in the original proposal didn't make the cut in the revised version, which was reduced $75.5 million.
Corroon clearly wanted a larger expenditure but seemed satisfied with the compromise proposal.
"This is one of the most important projects during my time as mayor, even though I won't be here to see it through," he said. "Now is the best time for parks construction: low interest rates and construction costs."
Councilman Arlyn Bradshaw said the council "should admire Corroon for his tenacity on the subject and coming up with something that can work for us."