The British leader toured European capitals on Tuesday in an attempt to salvage the deal, after MPs savaged its provisions on the issue of the Irish border.
May said she wanted "assurances" from EU leaders that if Britain ever entered the so-called "backstop" arrangement for the border, this would only be "temporary".
But she also said it was "the best deal available", adding: "There's no deal available that doesn't have a backstop".
She received sympathy from EU partners but firm rejections of any attempt to reopen the agreement, which was approved by EU leaders last month following tortuous negotiations.
"There is no room whatsoever for renegotiation but of course there is room, if used intelligently, to give further clarification," European Commission President Jean-Claude Juncker said ahead of talks with May on Tuesday.
German Chancellor Angela Merkel said there was "no way to change" the deal after meeting May.
Meanwhile, EU President Donald Tusk said bloc leaders wanted to help the prime minister but added: "The question is how".
May on Monday told MPs she was postponing a critical vote on the deal scheduled for Tuesday, admitting that it faced rejection and promising to consult EU leaders in an effort to get additional reassurances on the backstop.
She has said the vote will now be held before January 21.
On her whistlestop tour, she also met Dutch Prime Minister Mark Rutte and is headed to Dublin on Wednesday for talks with Irish Prime Minister Leo Varadkar before an EU summit on Thursday.
"I doubt if she really knows what she's going to achieve," said Pippa Catterall, professor of history and policy at the University of Westminster.
Catterall said that May could be trying "to take it down to the wire... so in the end parliament is faced with the choice: my deal or no deal".
After her weekly Prime Minister's Questions at 1200 GMT, May will chair her first cabinet meeting since she announced the vote delay where ministers will discuss stepping up preparations for a no-deal Brexit.
If no deal is approved by parliament, Britain will crash out of the European Union on March 29 -- a prospect that could trigger economic chaos.
The main opposition Labour Party has said the government is in "disarray" but is so far holding off on pushing ahead with a no confidence vote to attempt to topple May.
The Scottish National Party and the Liberal Democrats, which are both anti-Brexit, have urged Labour to do so and are hoping this could lead to a second referendum.
A few EU supporters within May's own Conservative Party are also calling for another popular vote, while Brexit hardliners are urging fellow Conservative to oust her.
A lot will hinge on what the Democratic Unionist Party, whose 10 MPs prop up the government, will do.
The DUP have indicated they will not vote against May on a confidence motion for now but have demanded that she jettison the backstop.