There are rumblings that he'd likely have the support of enough of them. Certainly more than Corbyn does from the Tories.
They might back him if they felt he could be trusted not to exploit the system for his own ends and to instead negotiate a reasonable deal in good faith and hold a second referendum.
The thing is that Brexit has mainly been scuppered by May's "red lines". The Brexit that was originally promised by the Leave campaigners included things like staying in the customs union and retaining free movement. It was May who decided that a hardest-of-hard Brexits was the only possible path.
I think, at this stage, that most MPs would back a deal that didn't do too much damage to the UK, regardless of whether or not it's something they actually want - because they understand what the realistic alternatives are.
One way to make it work is to negotiate a Brexit that's more or less a Brexit-in-name-only, leaving us not dissimilar to Norway. Part of this leaving deal includes a timeline stretching over a period of years for slowly pulling out of other aspects of the EU. This reduces the negative impact of Brexit, allows the Brexiteers to claim that they've won (even if they don't feel like they have) and leaves everybody in a situation that they're not entirely happy with but can live with.
It can be sold to the public as something that's over and done with and all the continuing negotiations can go on in the background. More than that, they can be quietly forgotten and life can go on as normal, should that be what a future government wants. We could even re-join the EU at some point in the future relatively easily and perhaps even without much attention being drawn to it. Any further withdrawal or re-joining could even be sold as if it's a different matter entirely.
We'll still be worse off than we currently are, but everybody gets to save face, everybody gets to convince themselves that they've won, the damage is reduced as low as it possibly can be, and everybody can get on with their lives. It's far from ideal, but it's something that I think most MPs and most of the public could live with.