The campaign group FairFuelUK previously said it believed the tax hike could will raise only £800 million, compared to Treasury projections that it would bring in £1.5 billion.
It could also cost as many as 35,000 jobs, it said.
The group will be campaigning at parliament today ahead of the debate and vote in the Commons.
Its spokesman, broadcaster Quentin Willson, said: "The momentum building up behind FairFuelUK's call to see this damaging 3p rise scrapped is becoming unstoppable.
"The Treasury appears to be listening. We welcome Labour pushing on this issue. Consumers are currently paying an eye-watering 80p-per-litre in combined fuel duty and VAT.
"This is socially unjust and adding another 3p in tax doesn't make sense for economic recovery and deficit reduction."
More top news
The heavy showers will ease off this weekend.
Labour MPs are attempting to build a consensus for a single challenger to Corbyn, while the big game in the Tory Party is Stop Boris.
Hefty showers and longer, slow moving downpours into this evening and again on Saturday - some lively with thunder.