Go for a hard Brexit, securing controls on immigration but abandoning hopes of access to the single market.
The likes of Liam Fox, Andre Leadsom and Priti Patel would cheer but the business lobby (and the bulk of Tory donors) would disapprove, not to mention London, Scotland and Northern Ireland. And there might be nasty economic repercussions. Would it command the support of the Commons?
Go for a soft Brexit, securing access to the single market but at the expense of free movement of labour (perhaps with minimal concessions) and payments into the EU, some kind of arrangement not dissimilar to Norway or Switzerland
The Tory right wing would scream betrayal, endangering the already slim Tory majority. And the people might ask what was the point of the whole exercise.
Keep on delaying the invocation of Article 50 in the hope that something - a general election? the collapse of the euro? Jean-Claude Juncker falling under a bus? - turns up. In other words, kicking the can down the road.
Nobody would be happy, particularly in the light of the continuing uncertainty, but they might be less unhappy than would otherwise be the case.
No easy answers then. But sooner rather than later, Mrs May will have to choose.