She could preside over a "No Deal" rupture with Europe tantamount to a declaration of economic war against the EU and risk a 2008-level economic crisis accompanied by a border upheaval in Ireland that could reignite the "troubles". Or she could break her extravagant promises to honor the "people's instruction" from the 2016 referendum and allow a new popular vote that might cancel Brexit.
The obvious answer would be to present voters with all three options No Deal, May's Deal or No Brexit.
That would be completely unacceptable to Brexit supporters, who would be guaranteed to lose if their voters were split between May's Deal and No Deal.
For example, the ballot could first ask voters to state whether they accepted the government's Brexit proposal, and then to answer a second conditional question: If the government's deal does not win majority support, would you prefer No Deal or remaining in the EU? Alternatively, voters could be asked, first, whether they want to remain in the EU or go ahead with Brexit, and then, in the event that Brexit wins, whether they would prefer May's Deal or No Deal.