The question now is whether she can come up with a strategy that is both achievable - and acceptable to her Cabinet, her party and her country - before she goes into battle with the European Union. The EU has proposed that the 31st of December 2020 is a more realistic final end of UK's membership of the EU.
The group of 62 lawmakers demanded a tougher approach in a number of areas, including "full regulatory autonomy" outside the European Union and the ability to start negotiating trade deals "immediately".
Talks aren't due to begin until next month, but look increasingly likely to start with a stalemate.
He said: "Yes we are aligned as 27 and yes we have very close ties with Britain". The hard part is getting the other side to agree. "We've set out our position, the Commission will set out theirs".
Although seen as a possible neat compromise for divided factions of the UK Government, the European Commission has already said "the "three baskets approach" [is] not compatible with the principles in the European Council guidelines". From the very start it has been a key principle of the European Union 27 that there can be no cherry-picking and no single market a la carte.
Non-EU citizens arriving in the United Kingdom, meanwhile, totaled 285,000 last year - an increase of 26,000 from the previous year.
The danger for May comes not with agreeing to set out ambitious demands, but if it becomes clear that there will have to be compromises.More news: Florida officer who didn't enter school during shooting now has armed guards
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Not only is the future of the country at stake, but the very future of Mrs May's administration if she, and her top team, are unable to reach an agreed position that reconciles Tory party splits. The auto sector is key because of its sensitivity to regulation and cross-border trade.
Germany's expected next government said in its coalition agreement it was willing to pay more.
Ministers also talked about the overall future partnership in a discussion led by May, and pro-Brexit Trade Secretary Liam Fox led a session on digital trade, according to May's office.
The lengthy Chequers meeting included dinner which consisted of a starter of cream of sweetcorn soup, ham hock croquette and cured duck and egg yolk, followed by a main course of slow braised Guinness short rib of Dexter beef with onions, parsnip mash and root vegetables, with a dessert of lemon tart with raspberry sorbet and fresh raspberries.
It is pressing for a status-quo transition period, which Brexit campaigners fear will see Britain subject to new European Union laws that could threaten the status of London's financial centre.
"There are a few Conservative MPs who just don't seem to want to accept what the British people wanted and because of the Parliamentary arithmetic if Labour decide to play party politics they could block things as well, so she's got some difficulties".
Labour leader Jeremy Corbyn is to unveil a competing vision of how Brexit should work in what is being billed as a significant address on Monday.