May told the House of Commons that "the vast majority" of issues had been settled, including the status of Gibraltar, Britain's territory at the tip of the Iberian Peninsula.
She said there is just "one real sticking point left" — the border between the U.K.'s Northern Ireland and EU member Ireland.
"We cannot let this become the barrier to reaching the future partnership we all want to see," May said.
May faces growing dissent from her political opponents — and, more worryingly, her own Conservative Party — over her blueprint for separation and future relations with the bloc.
Grumbling has grown since she suggested at an EU summit last week that Britain could remain bound by the bloc's rules for two years or more during a transition period after it leaves on March 29, to help solve the border problem.
London and Brussels agree there must be no customs posts or other barriers that could disrupt businesses and residents on both sides of the border and undermine Northern Ireland's hard-won peace process. But they do not agree on how to achieve that.
The EU has proposed keeping Northern Ireland in its customs union after Brexit, eliminating the need for border checks. But Britain says that is unacceptable because it would mean checks between Northern Ireland and the rest of the U.K.
May said the EU had shifted and was "actively working with us" on a British counter-proposal that would keep the whole U.K. in a customs union with the bloc.
Britain says any such arrangement must be temporary, while the EU insists the border "backstop" guarantee can't have a time limit.
May said she believed a solution could be found, but "serving our national interest will demand that we hold our nerve through these last stages of the negotiations, the hardest part of all."
Britain and the EU say they remain hopeful of striking a deal this fall, so that relevant parliaments can approve it before Brexit day. But May's room for maneuver is limited by pressure from pro-Brexit Conservatives and her government's Northern Irish ally, the Democratic Unionist Party, who oppose any more compromises with the EU.
She's also opposed by pro-EU lawmakers who want to keep close ties with the bloc after Brexit.
Amid talk of a leadership challenge, criticism of May has grown increasingly intemperate. Weekend newspaper headlines saying the prime minister is entering "the killing zone" and faces a metaphorical knifing drew sharp rebukes.
Conservative legislator Sarah Wollaston tweeted to condemn the "disturbing & violent language" used by some of her colleagues.
May said it was "incumbent on all of us in public life to be careful about the language we use."
Conservative lawmaker Grant Shapps said the coming week would be dangerous for May, as pro-Brexit Tories pondered whether to try to oust her.
Party rules state that if 48 Conservative lawmakers — 15 percent of the total — submit letters to a party committee calling for a no-confidence vote in the leader, one must be held. Only the head of the committee knows how many have been sent in so far.
"It's fairly high on the scale" of risk, Shapps told the BBC. "But she operates at the upper end of that scale almost every day of her life and remarkably, walks out at the other end."
With the Brexit clock ticking, fears are growing that Britain could crash out of the European Union without an agreement, an outcome that could create chaos at the borders and in the EU and British economies.
The Confederation of British Industry says a majority of U.K. firms are poised to implement Brexit contingency plans by Christmas, steps that could include cutting jobs, adjusting supply chains outside the U.K., stockpiling goods and relocating production and services overseas.
This story has corrected the surname of lawmaker Sarah Wollaston.