MPs will vote on Theresa May's Brexit deal later after she says she secured "legally binding" changes following last-minute talks with the EU.
The PM said the changes meant the Irish backstop - the insurance policy designed to avoid a hard border in Ireland - could not "become permanent".
She insisted that she had delivered what Parliament asked her to do.
Tory Brexiteers and the DUP are taking legal advice on the changes but Labour said the PM had secured nothing new.
The last time Mrs May's withdrawal agreement was put to Parliament in January, it was voted down by a margin of 230.
The BBC's political editor Laura Kuenssberg said it would be a "political miracle of historic proportions" if Mrs May could overturn such a heavy defeat.
She said the legal arguments were set to "rage" all day, with Attorney General Geoffrey Cox expected to update his advice on the deal, as he faces pressure to appear in person before MPs.
What was agreed?
Two documents were agreed after Mrs May flew to the European Parliament on Monday with Brexit Secretary Steve Barclay for last-minute talks with Mr Juncker and EU chief Brexit negotiator Michel Barnier.
The first is a "joint legally binding instrument" on the withdrawal agreement which the UK could use to start a "formal dispute" against the EU if it tried to keep the UK tied into the backstop indefinitely.
The other is a joint statement about the UK and EU's future relationship which commits to replacing the backstop with an alternative by December 2020.
Mrs May is expected to chair a cabinet meeting on Tuesday morning before the motion is debated in the Commons in the afternoon and votes are held in the evening.
Many MPs fear the backstop would keep the UK in a customs arrangement with the EU indefinitely.
After talks with Mr Juncker, the prime minister said she "passionately believed" the new assurances addressed their concerns.
"MPs were clear that legal changes were needed to the backstop. Today we have secured legal changes," she said. "Now is the time to come together to back this improved Brexit deal."
The Democratic Unionist Party, whose support Mrs May relies on in the Commons, said it would be "scrutinising the text line by line" before deciding whether to back the deal.
The Irish Prime Minister Leo Varadkar said the new agreements were an "unambiguous statement" of both sides' "good faith and intentions" - although he made clear they did "not undermine" the principle of the backstop or how it might come into force.
Nevertheless, ex-Brexit Secretary David Davis indicated he might be willing to support the deal if Mr Cox endorsed it, telling LBC if the attorney said it had legal force, it might "make this just about acceptable to me".
Monday morning government blues have been replaced by Tuesday morning nervous hopes.
The government does not suddenly expect its Brexit deal to be ushered through at speed, cheered on by well-wishers.
It does, however, believe that Monday night's double act in Strasbourg by Theresa May and Jean Claude Juncker puts it, to quote one cabinet minister, "back in the races".
The extra assurances wrought from weeks of talks with the EU will move some of the prime minister's objectors from the "no" column to the "yes".