He added that Britain's only path to avoiding a so-called "hard Brexit", in which London exited automatically on March 29 with no transitional arrangements in place to ensure the continued flow of goods, medicines and transport links, was to accept the existing deal.
She said: "When I return to Brussels I will be battling for Britain and Northern Ireland".
The EU has said the deal can not be renegotiated.
Writing in the Sunday Telegraph, Mrs May said: "While replacing the backstop with alternative arrangements was one option, [Sir Graham] would also be happy with the current backstop if there was a time limit or unilateral exit mechanism".
"Trouble ahead. Leave-backing MPs voted to support alternative arrangements in NI but with grave misgivings about the whole agreement", he tweeted on Sunday.
Under the terms of the deal, the United Kingdom would remain in the customs union until an alternative arrangement is found that ensured the avoidance of a hard border.
With less than two months to go until it automatically leaves the bloc, Prime Minister Theresa May's government has yet to agree an exit agreement or a position on its desired future relationship with the soon-to-be 27-member EU.
Japanese carmaker Nissan canceled plans to build its new X-Trail SUV in Britain, saying while it had taken the decision for business reasons the continued uncertainty around Britain's future European Union ties was "not helping companies like ours to plan for the future".
The backstop would kick in if Britain and the European Union have not agreed a trade deal on their future relationship after a time-limited transition period of up to two years.
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The draw presented Atletico Madrid, playing on Sunday, the chance to close the gap at the top to three points. Messi goal vs Valencia: Lionel Messi pulled things at level on the 64th minute with a brilliant strike .
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Tesla last disclosed in May that net Model 3 reservations - accounting for new orders and cancellations - exceeded 450,000. Tesla recently laid off some of the Model S and Model X staff and discontinued the cheapest versions of these vehicles.
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At present, Hernandez faces a mandatory minimum sentence of 47 years, ahead of potential reductions for his cooperation. The rapper admitted at a court hearing last week to being a member of the Nine Trey Gangsta Bloods, a group the U.S.
The prime minister rejected accusations that plans to reopen the backstop talks risked upsetting the Irish peace process.
"Nor do I have time for those who believe the verdict passed by the British people in 2016 should be overturned before it is even implemented", she added, referring to the rump of MPs calling for a second referendum.
"I'm determined to deliver Brexit, and determined to deliver on time -- on March 29, 2019", she wrote.
Reiterating his call for MPs to get behind the PM's deal, he said those in power have a duty to listen to "all voices in Northern Ireland" and reminded them of the "difficult - and sometimes tragic - road" the Irish and British governments had travelled to arrive at a solution which brought The Troubles to an end.
It came after a report claimed that Nissan was preparing to scrap plans to build its X-Trail 4×4 at its Sunderland plant.
Our political correspondent Chris Mason said that while Mrs May pledged to "go back to Brussels to secure a plan that Parliament can stand behind", the European Union remains publicly opposed to changing the backstop.
Mrs May found herself with some rare good news on Sunday after a new opinion poll suggested the Tories had moved into a seven-point lead over Labour.
But Downing Street denied reports in the Mail on Sunday that Mrs May's team are planning for a general election on June 6 - the 75th anniversary of D-Day.