A group of Tory MPs known as the European Research Group (ERG) said in a statement that the revisions didn't address their concerns that the United Kingdom had no way out of the backstop.
May flew to Strasbourg, France, late Monday for talks with European Commission President Jean-Claude Juncker.
May said after meeting Juncker: "The attorney general will set out in legal analysis the meaning of the joint instrument and unilateral declaration to Parliament".
"In politics, sometimes you get a second chance".
May said the new wording "will guarantee that the European Union can not act with the intent of applying the backstop indefinitely".
The so-called "backstop" solution for the Irish border - created to avert sectarian violence from returning to Britain's Northern Ireland - is opposed by more ardent Brexit backers.
Many fear that Brexit will divide the West as it grapples with both the unconventional USA presidency of Donald Trump and growing assertiveness from Russian Federation and China, leaving Britain economically weaker and with its security capabilities depleted.More news: Messi stars as Barca reach Champions League quarters
Pro-Brexit U.K. lawmakers said they would read the fine print and wait for the judgment of Britain's attorney general before deciding how to vote on Tuesday.
Two documents were agreed after Mrs. However, the text of the 585-page withdrawal agreement remains unchanged.
This is also a reiteration of the main Brexit divorce deal agreed in November.
It says that if the two sides aren't able to conclude a free-trade deal that supersedes the backstop "nothing in the Withdrawal Agreement would prevent it from instigating measures that could ultimately lead to disapplication" of backstop obligations.
"The further agreement yesterday provided additional clarity, reassurance and guarantees sought by some to eliminate doubt or fears, however unreal, that the goal was to trap the United Kingdom indefinitely in the backstop", Varadkar said.
"I am very, very suspicious and concerned about the time scale", Conservative lawmaker Andrew Bridgen said.
He called on the House of Commons to accept the deal "because I don't see further chances for negotiations".More news: Abbas aide blasts U.S. report that drops references to Israeli 'occupation'
"It is not, these doubts and fears can be put to bed, " he said.
One said: "He was going for "mechanism" Paul and you know it". "We have also made a declaration as a nation that, should the European Union behave in that way, that is exactly what we will do".
Cox's legal opinion came as I was on air live with my latest trader sentiment webinar so I discussed the markets' reaction as well as market sentiment more generally.
"It will be published".
The move is aimed at addressing the concerns of hard-Brexiteers in her own Conservative Party and the Northern Irish Democratic Unionist Party (DUP), which provides her government with its majority in the House of Commons.
Attorney General Geoffrey Cox in the Commons, urged the DUP's Nigel Dodds to back the deal. Both lawmakers and the public remain split between backers of a clean break from the European Union and those who favor continuing a close relationship, either through a post-Brexit trade deal or by reversing the June 2016 decision to leave.More news: Hashim Amla granted leave, Reeza Hendricks recalled