Meanwhile Labour is throwing their support for the Cooper Amendment
FT's political correspondent just reported that a Cabinet minister is "convinced that No. 10 will back Malthouse", citing unnamed sources. Meanwhile, the BBC, Sky News, and The Telegraph are following up with the earlier story here that Labour will be backing the Cooper Amendment, though it is said that they only want the extension to be 3 months instead of the proposed 9 months.
At this point, all May is trying to do is secure a majority so that she can get a win on the Brady Amendment. That at least gives her a reason to bring back to Brussels in saying that "look, this is what my parliament wants and if we want a deal, then the backstop has to go".
UK parliament members are likely well aware of that and all they are trying to do is find some insurance that May won't be able to threaten a no-deal Brexit outcome. Hence, there's also some strong support for the Cooper Amendment since if approved and parliament passes the bill, it would be an obligation for the government to extend Article 50 if it doesn't secure a deal by 26 February.
Regardless, if the European Union insists that they aren't going to change their red lines with regards to the backstop (which means they won't renegotiate the withdrawal agreement), whatever discussion on the Brady Amendment and the 'Plan C' isn't going to go anywhere at the end of the day.
All that means is further Brexit uncertainty for the UK economy and I reckon if both amendments get approved, it would be a positive immediate reaction for the pound but a negative follow through in the near-to-medium term.
Sure, odds of a no-deal Brexit is pushed further away and that means the likelihood of a second referendum is increasing. But given that May will want to push forward with 'Plan C' means that she will continue to rule out a second referendum and discussions with the EU will drag on further down the road, leaving the UK economy and BOE in deeper Brexit limbo.