While officials choreograph the first withdrawal of a sovereign state from the EU, it remains unclear whether May can get any deal approved by the British parliament.
"We are almost within touching distance now," Cabinet Office Minister David Lidington told BBC radio. Asked if he was saying a deal was possible in the next 24 or 48 hours, he said: "Still possible but not at all definite, I think pretty much sums it up. Cautiously optimistic."
A British government source said an agreement on a withdrawal deal was closer than it had been on Monday, after negotiators worked late into the night at the European Commission's modernist Berlaymont building in Brussels.
Sterling, which has see-sawed since reaching $1.50 just before results of the 2016 referendum vote for Britain to leave the EU, jumped almost 1 percent to $1.2972.
Brussels wants to get agreement on a draft deal by the end of Wednesday at the latest if there is to be a summit this month to approve it, although few in Brussels seemed to hold out much hope that a breakthrough could come this week.
The EU and the United Kingdom need an agreement to keep trade flowing between the world's biggest trading bloc and the fifth largest national economy.
But May has struggled to untangle nearly 46 years of membership without damaging trade or upsetting the lawmakers who will ultimately decide the fate of any deal she can secure.
Delaying approval of a deal by EU leaders until their next scheduled summit on Dec. 13-14 would shift the timetable close to the British parliament's Christmas holiday which is scheduled for Dec. 20-Jan. 7, potentially pushing the vote into the new year.
May told senior ministers in her cabinet on Tuesday that good progress had been made, a spokesman said, adding that a small number of outstanding issues remained.
It is unclear when the cabinet will be called to discuss a draft withdrawal agreement struck with the EU, or the outline of the future relationship.
But the intricacies of any deal are unlikely to stem the growing opposition to May at home: Brexit-supporting opponents fear she is signing up the United Kingdom to EU subjugation.
Brussels diplomatic sources said the bloc was trying to cajole May into sealing a deal this week and rubber-stamping it later this month, fearing that any delay would increase the chances of rejection by her ministers or parliament.
The European Commission has piled pressure on May by advancing contingency preparations for a no-deal Brexit.
With less than five months until Britain leaves the EU, the so-called Northern Irish backstop is the main outstanding issue.
But one EU diplomat said the entire European single market, and the freedom of citizens to live anywhere in it, were at stake. "The issue of Ireland is not about Ireland itself, it's just the tip of the iceberg," said the diplomat.
"It's about the single market and freedom of movement – it’s about no less than the EU’s future. If we drop Ireland now, that casts a long shadow on the EU’s future."
London's proposal for an all-UK customs arrangement must ensure that Britain follows EU rules on state aid and competition, labour rights and environmental standards.
Also in debate is the duration of the backstop. The EU does not want to allow London to terminate it unilaterally. London said the backstop would have to be temporary.
By seeking to leave the EU while preserving the closest possible ties, May's compromise plan has upset Brexiteers, pro-Europeans, Scottish nationalists, the Northern Irish party that props up her government, and some of her own ministers.
"No one is fooled by this theatre. Delay after staged-managed delay," former foreign secretary Boris Johnson said. "A deal will be reached and it will mean surrender by the UK."
Johnson, a prominent Brexit campaigner who resigned from May's government in July over her strategy, said the deal would turn Britain into a colony of the EU. (Additional reporting by Elizabeth Piper in London; writing by Guy Faulconbridge, editing by David Stamp)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)