According to the Daily Mirror today, 10 January:
"Theresa May is hoping to win the support of Labour MPs for her Brexit deal by backing key guarantees on workers’ and environmental rights.
"The Mirror understands the Government is likely to support an amendment put down by Labour MPs who could be open to backing her in the crunch vote next week.
"As many as 20 Labour MPs, most of them with Leave voting seats, could rally behind the Prime Minister's plan if she throws Downing Street's weight behind the move.
"Bassetlaw MP John Mann told the Mirror that the amendment would make Mrs May’s deal 'more attractive' and tackle key Labour concerns.
"Caroline Flint, MP for Don Valley, added: 'Given the government cannot rely on the hard Brexiteers on their side, they have to reach out across the House to Labour'."
- the "withdrawal deal" commits the UK to keeping all EU rules, including on workers' rights and the environment, until end-2020 or maybe 2022
- the Tories' own "declaration on future relations with the EU" already commits vaguely to a "level playing field" on such issues; and
- big business and the bulk of the Tories have no immediate wish to scrap such EU rules - they have learned to live with them, and the costs of scrapping them in clogging up trade with the EU exceed the benefits (to them)
it will be no surprise if May backs the amendment, the amendment won't change much, and it certainly won't stop the Tories trashing social rights further down the line.
What Mann and Flint may do is enable the Tories to get Brexit "over the line".
The Labour leaders are ill-placed to combat Mann and Flint, since they themselves have been backing Brexit (covering that with blather about tweaks to the Tories' deal).
The usually well-informed Labour List website reports https://labourlist.org/2019/01/could-a-workers-rights-amendment-win-labour-backing-for-mays-deal/:
"Although Gareth Snell wrote a piece for LabourList in November pledging to vote against May's deal, he has now proposed an amendment with Caroline Flint, Lisa Nandy and John Mann that would guarantee workers' rights and environmental protections. It is expected that the government will back this helpful move. And the talk is now of May ultimately conceding on customs union membership.
"Could that see the Labour leadership abstain or support a revised Tory deal? Remember that the only way to get the DUP to vote with Labour in a vote of no confidence is for May's deal to pass. If a general election is Corbyn's first preference, letting a Plan B gain Commons approval could be the next step.
"Update, 11am: LabourList has been told by Snell’s office that the MP still intends to vote against May’s deal, and the amendment relates to 'the conversation about future domestic legislation' – not getting her deal passed".
Jeremy Corbyn: off the fence! Back a "People's Vote"! Back Remain!
Postscript 11 January: A look at the Fixed Term Parliaments Act confirms the off-the-wall character of the "abstain on the withdrawal deal in order to get the DUP to vote no confidence" tactic.
It also confirms the folly of excessive delay before putting a motion of no confidence.
The Act says that if the government is forced into an early general election by two votes of no confidence 14 days apart, then the date of that election is set by the Queen "on the recommendation of the prime minister".
In 2017 the early general election was called for a date 52 days after the parliamentary vote for it. There would be no legal bar on the Tories adopting a longer delay. 52 plus 14 makes 66, and 66 days before 29 March, which is day 88 of the year, takes you to 22 January, which is the earliest day Skwawkbox reckons possible for a vote of no confidence. Then the general election would be on 29 March, and by the time the results were known, Brexit would have happened...