The Tube handles four million journeys every day, meaning many overground trains and buses become packed during the strikes.
Nearly all Tube stations in Zone 1 are expected to close and a "severely reduced" service run across the rest of the Underground from Sunday at 6pm and throughout Monday if the strike goes ahead.
Transport for London (TfL) has warned the majority of central London Tube stations will be closed and there will be "limited services" in outer London if the strike goes ahead.
Key Network Rail stations including Victoria, King's Cross, Waterloo, Paddington, Euston, Bank and London Bridge, will have no Underground connections.
'As a result of the management failure to face up to the current crisis the talks have collapsed and all industrial actions remains on'.
He said: "We've been in with ACAS and London Underground all week long and basically their position hasn't moved all the way through".
An RMT spokesman told the Press Association that the hundreds of job cuts agreed by former London mayor Boris Johnson had been a "disaster" and should be reversed.
The unions met LU bosses earlier this week under the chairmanship of the conciliation service Acas but said no progress had been made.
Steve Griffiths, chief operating officer for LU, said there was "no need" for the strike, promising the recruitment of around 500 staff this year, the BBC reported.
"We will continue working with the unions, as well as implementing recommendations made by the London TravelWatch review, to ensure our customers feel safe, fully supported and able to access the right assistance at all times".
"We encourage the trade unions to continue working with us in order to resolve this dispute and deliver the customer service our customers expect".
Anyone planning on travelling to Heathrow Airport should be aware that Piccadilly line services will still run between Hammersmith and Terminals 1, 2 and 3, but there will be no service to Terminals 4 or 5.
If it does go ahead, many tube stations in zone 1 will be shut.
He added: 'Frankly, it doesn't appear that London Underground is serious about resolving this dispute.