The Foyle MLA said that a two week timeline is not enough to substantially alter negotiations.
He said: “Following a third successive defeat of Theresa May’s deal, it’s time to face up to the fact that this iteration of Brexit is dead in the water.
“What’s needed now is a long extension to the Article 50 period for all parties to calmly and rationally reflect on where we go from here.
“The grotesque political circus at Westminster needs to stop.
“Our first preference is to revoke Article 50 and provide people with an opportunity to fundamentally reconsider this whole sorry saga.
Brexit is a negative constitutional and economic event. What we have experienced over the past two years has been damaging not just to the financial and economic security of people and communities but to our social fabric.
“But if the British Government won’t see sense and they remain committed to a damaging path toward Brexit, they need to realise and the DUP needs to realise that there is no outcome where the European Union or the Irish Government renege on their commitment to protecting Northern Ireland. No amount of brinkmanship will weaken their resolve.
“In those circumstances, the only form of Brexit that is negotiable is one which sees Britain and Ireland remain in the customs union and the single market.
“That meets the mandate of the referendum result and the DUP red lines on economic and constitutional integrity. Theresa May’s government should call Nigel Dodds’ bluff and put it up to them.
“The SDLP will continue to pursue every avenue to prevent a hard Brexit and a hard border on this island.
“But the first step for all parties remains clear – a long extension to the Article 50 period for a fundamental rethink about our future,” added Mr Eastwood.