Unions are giving councils more time to come up with an improved pay offer in an attempt to avoid strikes which could close schools.
Unison had set a deadline of 17:00 on Wednesday, but local authority body Cosla asked for an extension as it sought extra money from the Scottish government to fund a deal.
Unison and Unite now say any new offer will need to be made by Thursday.
Cosla and the deputy first minister are due to meet later on Wednesday.
The Scottish government has previously said that councils would need to use existing budgets to fund a better deal.
The three-day strike by Unison, Unite and the GMB is scheduled to happen on 26, 27 and 28 September across 26 of Scotland's 32 council areas.
Unison wants a new offer by 12:00 on Thursday while Unite said it would give Cosla until 17:00 that day.
The GMB also said a revised offer must arrive on Thursday to avert the strikes.
