It is expected that Tuesday will see MPs decide whether Parliament should have the power to set the Government's negotiating goals if Theresa May's deal with Brussels is voted down.
Phillip Lee, Member of Parliament for Bracknell, stood down from his position as Justice Minister because he "couldn't support how our country's current exit from the European Union looks set to be delivered".
Theresa May has averted an embarrassing defeat over the government's EU Withdrawal Bill by giving MPs a say on the next steps for Brexit if she fails to secure a withdrawal agreement by the end of November.
The British government was rocked by a resignation and faced anger in Parliament over its Brexit plans, but staved off defeat by offering concessions to MPs who want to soften the terms of the UK's exit from the European Union.
Potential rebels fell into line after Solicitor General Robert Buckland said ministers were ready to "engage positively" with their concerns before the Bill returns to the Upper House next Monday.
Commenting after Tuesday's votes, Dr Lee said: "Delighted that the government has agreed to introduce an amendment to the EU Withdrawal Bill which will give Parliament the voice I always wanted it to have in the Brexit process".
The government won the vote after last-minute horse-trading, some of it in the open on the floor of the House of Commons - some behind closed doors. "A meaningful vote is not the ability to reverse the decision of the referendum".
Only 15 minutes was set aside for debating changes to devolved powers proposed by the Lords in the EU Withdrawal bill. Yet now, with just hours to go before the parliamentary showdown, the Prime Minister looks as though she has brought her administration back from the brink.More news: Dennis Rodman Tears Up While Discussing Trump's Meeting with Kim Jong
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At stake is her Brexit strategy and her ability to hold her party together as she fights to deliver a Brexit divorce deal in the next 10 months.
Pro-Brexit tabloid the Sun warned lawmakers on Tuesday's front page that they had a choice: "Great Britain or great betrayal".
If the government avoids defeat, is Brexit a done deal?
Another flashpoint could come when lawmakers vote Wednesday on an amendment seeking to keep Britain in a customs union with the EU.
The Daily Express, another pro-Brexit tabloid, issued a thinly-veiled threat to lawmakers, saying they should "Ignore the will of the people at [their] peril".
Conservative former minister Anna Soubry said the abuse of MPs who speak out against the government's Brexit policy "simply has to stop".
It is the legislation aimed at ensuring the United Kingdom has a smooth transition out of the EU.
'The goal of the EU Withdrawal Bill is simple - it is putting EU legislation into law to ensure a smooth and orderly transition as we leave, ' she is expected to tell them.