Councillor Davie Paterson made the comment at a meeting of the council last Thursday, when members agreed to call on Police Scotland to delay the withdrawal until 2016.
Councillor Paterson said: “People take a chance at the minute with the service we have now, but they will take even bigger chances on double yellow lines and other restrictions with no traffic warden service, and I think there is going to be a fatality.”
Conservative group leader Michelle Ballantyne said the removal of the wardens would be the start of a ‘slippery slope’ for town centre parking.
However Councillor Stuart Bell responded: “I think we have slipped down the slope already.
“The result of the survey in Peebles on on-street parking was staggering.
“People were parking in bays for 1.3 hours, when the limit is 45 minutes, for 2.8 hours on single yellow lines, and 1.4 hours on double yellow lines.
“The reality is that people are not stopping on double yellow lines and nipping in to a shop, they are staying there for quite some considerable time.”
Rob Dickson, director of environment and infrastructure, told the meeting: “We know at present, even with the traffic warden service, that there are existing problems with town centre parking.”
He added that council staff are working with COSLA and Traffic Scotland on how rules regarding authorities taking on decriminalised parking enforcement (DPE) may change to help rural councils, but warned it may take some time.
Currently councils have to show that they can run DPE as a break-even service at least, but officers believe this would not be possible in the Borders.