Many fans and drivers have made clear they are not happy with the change, designed to keep the title alive right to the end by offering twice as many points in Abu Dhabi next November.
"I think it's wrong," Toro Rosso driver Jean-Eric Vergne told Italy's Corriere dello Sport, "because it devalues the work a driver has done throughout the whole season.
"As drivers we are not excited about it," added the Frenchman.
Ferrari president Luca di Montezemolo, who has the power to veto key decisions in F1, has also emerged as an opponent of the rule.
"I would not be surprised if the rule is soon abolished," said the Italian.
To discuss this and other matters, Montezemolo has invited chiefs of the other F1 teams to a meeting at Maranello next month.
"There should be more dialogue between the teams when it comes to discussing the problems affecting Formula One," he said.
And the latest development is that F1 chief executive Bernie Ecclestone is also re-thinking the double points idea.
"It may well be that the rule is cancelled altogether at the next (strategy group) meeting in January," he revealed to the Telegraph newspaper.
But Ecclestone said that his preference is actually for the concept to be extended, with not just Abu Dhabi but also the preceding two grands prix attracting twice as many points for a thrilling end of season battle.
"I think it should be the final three races or nothing," he said.