"If we don't check out tonight, we may never leave", tweeted Conservative legislator Bob Seely.
"Turning the content of the 14 January letter from Donald Tusk and Jean-Claude Juncker into a joint interpretative declaration does not change that".
The latest pact stressed the "legal force" and "binding character" of the withdrawal agreement.
Attorney General Geoffrey Cox has dealt a serious blow to Theresa May's hopes of getting her Brexit deal through parliament, writing in new legal advice that the risk of being trapped in the Irish border backstop remains "unchanged" despite last-minute assurances.
However, a substantial defeat for the prime minister was likely to push sterling lower, he said.
The two sides have also published a "joint statement" which commits to replacing the backstop with "alternative arrangements" by the end of December 2020.
The second vote on May's Brexit deal, up until last night, was widely believed to be likely rejected.
The PM said this would outline the UK's position that there was nothing to prevent it from leaving the backstop arrangement if discussions on a future relationship with the European Union break down and there is no prospect on an agreement.
British lawmakers, who on January 15 voted 432-202 against her deal, were studying the assurances with lawyers. This is now extremely unlikely.
European Union pessimistic on Brexit vote but insists it's the last chance - worldwide
But, if MPs once again reject the PM's deal, May has warned a longer extension will be necessary to work out what to do instead. The pound fell sharply from recent highs plunging more than one per cent on the day against the euro.
Erdan: 'We will not allow a religious war caused on Temple Mount'
A fire rages in a police post on Jerusalem's Temple Mount after a Molotov cocktail was thrown at it on March 12, 2019. However, in February Palestinians opened the areas, breaking Israeli locks on an outer metal door that leads to them.
Browns' acquisition of Odell Beckham, Jr. could put them over the top
The Browns also decided they needed to find a game-breaking wide receiver who will make plays all over the field. Jabrill is a quality safety in this league and he is a legitimate linchpin on the back end of our defense.
In a statement the DUP said it would scrutinise the text from Mrs May's meeting "line by line". The British government states it has secured "legally binding changes" from the E.U.to address concerns about the border between Ireland and British-controlled Northern Ireland - a main factor in the rejection of the deal earlier this year.
The signs don't look great though.
Steve Baker, a pro-Brexit member of May's Conservative Party, said the new agreement seems to fall "short" of the plan he wanted to see.
What Brexit votes are happening this week? As a result, GBP has dropped and risk appetite more generally has tumbled. This chart shows how the week may develop.
DUP leader Arlene Foster told the BBC she was sympathetic to demands for a day's delay to give time to study the assurances.
Britain's Prime Minister Theresa May speaks after the results of the vote on Brexit deal in Parliament in London, Britain, March 12, 2019.
If that happens, MPs will vote on Thursday on extending article 50 which triggered the UK's exit process from the EU.
If they vote for that, the Prime Minister will go to Brussels to ask for an extension, something that all 27 member countries will need to agree to. Interestingly enough, this managed to anger the House of Commons leader Andrea Leadsom, who pointed out that Barnier's option is actually a proposal thrown in by May and rejected months ago.
All 650 MPs in the Commons are eligible to vote, with a majority required to win a vote. The House Speaker and 10 other MPs do not take part in voting.