Theresa May has options:
1. Call A50 with a free vote. Might not pass, makes her look a bit inept if it doesn’t.
2. Call A50 with a whipped vote. Still might not pass, makes her look very inept if it doesn’t, especially if her own party rebels.
Even if the vote does pass, she still might get stuck in a protracted battle with the Lords, who are completely within their rights to reject A50 at the moment and aren’t so easily cowed into implementing stupid ideas. A lords defeat would be humiliating even if it was only the first battle.
But in either case she will have to define her aims before she can reasonably expect parliament and the lords to listen to her. Is it a hard brexit or a soft brexit? Clearly she’s trying to avoid a hard brexit otherwise she’d have committed to it by now, but she hasn’t specified this directly.
Brexiters are so divided that committing to either course of action will lose support and anger different factions of her party. So far she’s been reluctant to announce where she stands and one interpretation of this would be that she doesn’t think she can hold her party together once the infighting starts. She’ll find no cross-party support from sensible Remainers – divide and conquer is an effective tactic, so it is in any Remainer’s interests to let the different brexit factions battle it out amongst themselves.
3. Call an early election with brexit/A50 as a manifesto pledge to try to increase her majority such that A50 will more likely pass decisively. The lords by convention won’t challenge manifesto pledges, so this solves that problem. But any election will be fought on the brexit issue and that means opening her aims up to scrutiny. The same problem as above. Also, it would be a tactical faux pas to try to unsettle Corbyn before 2020; he’s a free 5 year extension to her residence in Number 10 – why waste that?
4. Ask parliament to call another referendum, this time making it well defined over the three options of hard, soft and no brexit, using a preferential voting system, and self executing. It would be undemocratic for MPs to vote against this as it would provide more information than the first, so no problems getting it through parliament, although some Leaver MPs will privately feel annoyed that they’ve been outmanoeuvred by their own “will of the people” rhetoric. This makes the country look idiotic, but that ship sailed some time ago.
This seems like the least likely option but it is also the only one that deflects responsibility away from her while staying in control. It has no more risk than any other option and significantly more pay off because 1. whatever the outcome she has a strong justification for it and 2. it’s the only option that legitimately puts “let’s go back to normal and forget this ever happened and shield myself from the long term risk of this all going terribly wrong and being remembered as the worst PM in history” back on the table. This is clearly her best option.