The legislation would require a delay to Brexit unless there was a deal or Parliament backed Britain leaving the EU without one by October 19.
Mr Johnson is proroguing Parliament next week, so MPs are desperately trying to rush through the bill before the suspension.
Here are the skirmishes that are anticipated and how events may play out over the tumultuous week in politics.
How can MPs legislate to prevent a no-deal exit?
The cross-party group of MPs will attempt to use a motion on Tuesday, which would allow them to control the Commons business on Wednesday, guaranteeing time to debate a new law to block a no-deal Brexit.
This could be achieved through an emergency debate being sought from Commons Speaker John Bercow under the rules of standing order number 24, commonly called SO24.
Is time of the essence?
Certainly, and the urgency has been exaggerated because of the prime minister's controversial decision to suspend Parliament shortly after MPs return.
Legislation would need to be debated and approved by both MPs and Lords, in a process that usually takes weeks, but could be hurried through in as little as three days.
The Commons is not scheduled to sit on Friday, but MPs could hold an emergency session to continue the no-deal debate and there has been speculation the Lords could sit over the weekend to get the legislation through.
September 9 is the earliest date Parliament can be suspended and September 12 the latest, while MPs are not due to return until October 14.
What exactly will MPs be voting on?
The legislation put forward by a cross-party group, led by the Labour MP and Brexit Select Committee chairman Hilary Benn and Tory former Foreign Office minister Alistair Burt would require a delay to Brexit, unless there was a deal or Parliament explicitly backed leaving the EU without one by October 19.
The snappily-titled European Union (Withdrawal) (No. 6) Bill 2019 also has the support of Tory former Cabinet minsters Philip Hammond and David Gauke, a sign of how the rebel ranks have been bolstered following the change in prime minister.
Under the terms of the Bill, the Government must ask the European Union for a delay to Brexit until January 31, 2020 if no agreement has been reached and MPs have not agreed to a no-deal exit.
If the European Council proposes an extension to a different date then the prime minister must accept that extension within two days, unless the House of Commons rejects it.
What has the Prime Minister said?
After an emergency Cabinet meeting, the Prime Minister used a statement in Downing Street on Monday to urge MPs not to back a “pointless” delay.
Such a move would “cut the legs out” from under the UK’s negotiating position with the EU.
It has been made clear to Tory MPs that they will lose the whip if they back the plan and, in a dramatic raising of the stakes, allies of Mr Johnson said he would seek a snap general election if Tuesday’s measure is passed.
Will there be an election?
A senior Government source said Mr Johnson could go to the country on October 14 – unusually for Westminster elections, that is a Monday rather than a Thursday – if he is defeated on Tuesday.
That would require the support of two-thirds of MPs under the provisions of the Fixed-term Parliaments Act, but some are reportedly suspicious the prime minister would seek to alter the election date to delay it until after Brexit.
Meanwhile Opposition leader Jeremy Corbyn said a vote of no confidence is “very much there on the table” as he pledged to “do everything we can to stop” no-deal.
If the vote won the support of a majority of MPs, there would be 14 days for another government to be formed, otherwise Parliament would be dissolved and a general election triggered.
Are there other ways the prime minister's plans could be thwarted?
The prime minister faces threats from many angles, with legal challenges coming in courts across the UK.
A cross-party group of MPs and peers who want to block Parliament’s suspension will have the full hearing of their application in Edinburgh on Tuesday.
On Thursday, the High Court will consider a judicial review request from Gina Miller, the businesswoman who successfully challenged the Government over the triggering of the Article 50 process to start the Brexit countdown.
She, too, wants to challenge Mr Johnson’s suspension of Parliament.
And in Belfast, a judicial review against the Government by a campaigner arguing that no-deal could jeopardise the Northern Ireland peace process is scheduled for September 16.