The UK's government flagship Great Repeal Bill, which plans to scrap the European Communities Act and put all current EU law onto the British statute book, will face "hell" as it passes through the Houses of Parliament, Theresa May was warned on Thursday 13 July.
Labour plans to amend the draft legislation in the House of Commons, while the Liberal Democrats could attempt to torpedo the bill in the House of Lords, where the Conservatives are outranked by opposition and crossbench peers.
"It is one of the most significant pieces of legislation that has ever passed through Parliament and is a major milestone in the process of our withdrawal from the European Union," said Brexit Secretary David Davis.
"By working together, in the national interest, we can ensure we have a fully functioning legal system on the day we leave the European Union.
"The eyes of the country are on us and I will work with anyone to achieve this goal and shape a new future for our country."
But despite Davis' and May's calls for contributions from opposition parties, the minority government is facing increasing pressure over its plan to stop the oversight of the European Court of Justice (ECJ) and a move to quit the European Atomic Energy Community (Euratom).
With the Tories being propped up by their "confidence and supply" agreement with Northern Ireland's Democratic Unionist Party (DUP), a backbench rebellion from Conservative MPs could see the bill dramatically changed and May's premiership come to an end.
"We have been learning the lessons of Maastricht and I am putting the government on warning. If you found the Article 50 bill difficult, you should be under no illusion, this will be hell," said Tim Farron, the outgoing Liberal Democrat leader.
"If the government try any wheeze or trick to force through changes to vital protections, from workers' rights to the environment, they are playing with fire. I am keen to work across party lines to do everything we can to protect these rights.
"If this Tory Brexit government and their Labour cheerleaders think this will be waived through, they have another thing coming."
The comments came as Labour leader Jeremy Corbyn and Shadow Brexit Secretary Sir Keir Starmer plan to meet with chief EU Brexit negotiator Michel Barnier in Brussels.
"Labour respects the referendum result and the decision to leave the European Union," Corbyn said. "But a Labour Brexit would look very different to the race-to-the-bottom tax haven backed by this Conservative government.
"In contrast to the Conservatives' megaphone diplomacy, we will conduct relations with our European neighbours respectfully and in the spirit of friendship. Our strong links with our European sister parties gives Labour an advantage in reaching an outcome that works for both sides.
"Labour would negotiate a jobs-first Brexit deal which puts the economy, jobs and living standards front and centre. Labour would unilaterally guarantee the rights of EU citizens living in the UK because it's the right thing to do."