I doubt the outcome would be different. We would still be voting while under austerity measures. The vast majority of people in this country are struggling to make ends meet as it is under the Tories. They are not going to vote to stay in the EU when in their eyes the EU has been painted as having delivered them nothing. Add to the fact that this time they'll have a government supporting the deal* and an opposition led by Wishy Washy who have no idea whether they are in or out, and you've got a Leave vote.
*Interestingly, should there be a second referendum (which I don't think there will be), what would May campaign for? One assumes, if she has the nation's interests at heart and having seen all the long-term economic indicators she would revert to her old position and campaign to stay - or will she save the Tory party first?
For a second ref May would have to resign.
I cant see it with her in charge, I say in charge....