Labour is 100% fucked.
To expand on that slightly...
- May just said that the agreement will go through the house. The Tory's majority is thin and the SNP and Lib Dems will oppose but Labour has a LOT of "Leave" constituencies. Even if they fully whip, it still requires some Tories to abstain or rebel, which *could* happen but...
- Even if it does fail to pass, it's considered a VoNC like losing a budget, May goes to the polls and absolutely stonks Corbyn to achieve an ~100 seat majority. It then passes with ease. So, eitherway, it's passing.
- Furthermore, Labour are in the unenviable position where they a) need to come up with their own position now and b) this plan will almost certainly involve a soft Brexit. This alienates the huge rafts of leave voters that would traditionally vote Labour, as well as Remain voters who see soft Brexit as throwing in the towel. They'll simultaneously suffer drains to the Lib Dems/Greens and UKIP from the same policy position!
- They have at least 2 years of this haemorrhaging of support to go before any general election is likely to take place.
- In one felled swoop the Tories have cut off a big part of UKIP's remaining allure by promising the end of free movement and a pretty unambiguously hard Brexit. Why still vote for a party who will never gain government? As such, less seats have the right vote split, whilst the left will be going several ways based on the voters' Leave or Remain stance.
For anyone aghast at hard Brexit but who still supports Corbyn, this is partially what happens when a government's main opposition comes from their own back benches.