The workplace parking levy was one of the key parts of a deal between the SNP and the Greens, enabling the minority administration to get its tax and spending plans through Holyrood in January.
Councils will be given the power to impose the tax through an amendment to current proposed transport legislation going through the Scottish Parliament.
The Scottish Conservatives claim the tax could cost workers up to £500 a year.
First Minister Nicola Sturgeon was among those to receive letters from angry SNP members vowing to pull support for the party over the planned tax.
The letters were revealed following a Freedom of Information request from the Scottish Conservatives.
One wrote: “I’ve voted for the SNP for the last 44 years... but this ridiculous tax on workers driving to work is totally wrong.”
They said driving to their workplace takes 15-20 minutes but would take an hour and a half and two buses to reach by public transport.
The person vowed to resign their party membership if the tax goes ahead.
Another wrote: “I have always been an SNP supporter and voter, a quick check would also confirm I was a party member.
“I do appreciate the Scottish Government say it’s up to local authorities to action the tax or not.
“However, I have absolutely no shadow of doubt that [SNP-run] Glasgow City Council and others will seize the opportunity to raise revenue via this unfair tax and it will fall on people like me to just stump up because employers won’t take the cost, for the simple reason - why would they?”
The shift worker said using buses to get work would add two hours to his commute.
A lifelong SNP supporter wrote to Transport Secretary Michael Matheson expressing “disgust” at the tax and vowing never to vote SNP again, saying the party comes across as “flippant and smirky”.
One charity worker said the charge would be “game over” for them as they cannot afford to pay.
She told Mr Matheson: “How could I and many like me consider voting SNP ever again?”
Another voter wrote: “This appears to have been added to the budget late, to get it through parliament, without really considering how it will affect employers and their employees.”
More than a dozen employees of airline Loganair working at Glasgow Airport wrote to Mr Mackay opposing the levy, saying: “It is unfair and unreasonable to impose a workplace car park tax when I have no realistic alternative to using my car.”
The GMB union also wrote opposing the tax, while the Scottish Association of Social Workers called for the NHS exemption to be extended to their staff.
Friends of the Earth Scotland and other environmental organisations wrote backing the tax, saying it will cut emissions and congestion.
Tory finance spokesman Murdo Fraser called for the levy to be scrapped.
He said: “After being inundated with views from members of the public, the SNP should be left in no doubt about just how unpopular this plan is.
“Hardworking people are outraged that they should be charged even more just for driving to work, and many simply cannot afford it.”
SNP MSP George Adam said: “The Tories’ hypocrisy and misinformation campaign on this issue has been brazen and, frankly, pathetic.
“The workplace parking levy is about empowering councils - allowing them to decide upon which policies work best for them.
“Local authorities already have such powers in Tory-run England and Tory councillors in Edinburgh voted for such powers only last year - showing their recent faux outrage up for the hypocrisy that it is.”