Quizzing the attorney general, Geoffrey Cox, in the House of Commons, Dodds said that under Monday night's Strasbourg deal, "provided there is not bad faith" behaviour from the European Union in future negotiations, the United Kingdom and Northern Ireland could be "trapped" in the backstop.
May had announced changes on Monday created to overcome lawmakers' concerns about provisions created to ensure the border on the island of Ireland remains open after Brexit.
Arriving in Bucharest, most EU European affairs ministers were upbeat about the deal which will be voted upon by the United Kingdom parliament Tuesday night.
The second meaningful vote on May's "improved" deal will take place on Tuesday in the House of Commons.
Many Brexiteers anxious that the backstop, aimed at avoiding controls on the border between the British province of Northern Ireland and EU-member Ireland, could trap the United Kingdom in the EU's orbit indefinitely.
The immediate reaction was cautious from Brexit-supporting lawmakers and from the Northern Irish Democratic Unionist Party (DUP) which props up her minority government.
In January the British Parliament rejected May's deal by 230 votes, the biggest defeat for a government in modern British history.
Mr Juncker said he had spoken to Irish Taoiseach Leo Varadkar, who he said had indicated he was "prepared to back this approach in the interests of an overall deal".
May flew to Strasbourg late last night to continue negotiations with European Commission President Jean-Claude Juncker, returning with the promise of further reassurances on the Irish backstop; but the legal instrument the Prime Minister delivered to MPs contained no new additions or amendments to the withdrawal agreement, which still makes no provision for the unilateral termination of the backstop.
The ultimate outcome remains unclear, though most diplomats and investors say Brexit will define the United Kingdom's prosperity for generations to come.
Hard-core Brexit backers in Parliament came to the same conclusion, saying they wouldn't support the deal in the House of Commons.
Three mistakes of Rishabh Pant that cost India 4th ODI
Kohli was referring to the incident that took place in the 44th over of Australia's innings. The fifth and final game will take place on March 13 at the Feroz Shah Kotla in Delhi.
Manchester United 'to appoint Ole Gunnar Solskjaer during global break'
We played well but they were always risky on the counter-attack and today with five at the back we were more compact. And their first loss in the Premier League came on Sunday away at Arsenal , almost three months after he took over.
Australia court jails cardinal for six years — George Pell
Pell, who was until late-February the Vatican's treasurer, is the highest-ranking Catholic to be convicted of child sexual abuse. Before walking back to the court's cells, flanked by security, Pell signed paperwork to be registered for life as a sex offender.
Britain is due to pull out of the European Union in less than three weeks, on March 29, but the government has not been able to win parliamentary approval for its agreement with the bloc on withdrawal terms and future relations.
"The attorney general has confirmed that there have been no significant changes to the withdrawal agreement despite the legal documents that were agreed last night", Labour Brexit spokesman Keir Starmer said.
Will Theresa May resign and will she be able to get her Brexit deal through Parliament?
If politicians vote down Mrs May's deal, she has promised a vote tomorrow on whether to leave without a deal and, if they reject that, then a vote on whether to ask for a limited delay to Brexit.
The main opposition Labour Party also maintained its opposition to the deal.
British MPs, who on 15 January voted 432-202 against her deal, were today studying the assurances with lawyers.
German EU affairs minister Michael Roth, called it "a far-reaching compromise".
Another defeat in parliament could see Britain sever ties with its closest trading partner on March 29 with no new arrangements, causing huge disruption on both sides of the Channel.
Even if the deal is approved, Brexit Secretary Stephen Barclay said there might need to be a "technical extension" so that all the needed laws can be passed.
"Today is our Hotel California moment".