Boris Johnson and David Davis have warned voting against the Government's Brexit bill would cause chaos, in an effort to bolster support for the legislation.
Foreign Secretary Johnson said defeat for the repeal bill - which transfers European Union rules and regulations into domestic laws - would result in a "disorderly and chaotic" departure from the bloc in March 2019.
His comments echoed those of Brexit Secretary David Davis, who stressed the British people "did not vote for confusion" in last year's referendum.
Labour will vote against the European Union (Withdrawal) Bill, arguing so-called "Henry VIII" powers in the Bill allowing ministers to alter laws without full parliamentary scrutiny amount to a "power-grab".
Last week Shadow Brexit Secretary Sir Keir Starmer said the bill would "reduce MPs to spectators", calling it "an unprecedented power grab".
The warnings from the senior Cabinet ministers are aimed at both wavering Labour MPs - particularly from Leave-backing seats - and Remain-supporting Tories.
Johnson told BBC Radio 4's Today programme "we need to get this great ship launched", with the transfer of EU laws on to the domestic statute book a key priority.
"If we don't do that then of course the whole thing will be disorderly and chaotic," he said.
"People who vote against it will be effectively voting to frustrate Brexit by producing a completely chaotic result."
His advice to the Prime Minister was "keep going, get this thing done". "What people want is a government that delivers on the priorities of the people," he added.
Mrs May's fragile grip on power in the Commons, relying on the votes of the DUP for a majority, could be boosted by an estimated dozen Labour rebels prepared to defy Jeremy Corbyn's orders.
Former minister Caroline Flint said that Labour MPs should work to improve rather than kill the Bill as she vowed not to oppose it.
The Don Valley MP said a defeat for the Bill would cause "huge problems" and told the Today programme: "I do believe that in respecting the outcome of the referendum, in respecting what I said to my electors in the general election just a few months ago, it is important that we get on with the job of making sure we can have as smooth an exit from the EU as possible."
The Liberal Democrats, who will oppose the legislation, have urged the Labour leader to sack any frontbenchers who defy the whip or risk his party's shift towards a "softer" Brexit being exposed as a "sham".
Several Tory MPs have expressed disquiet over the Bill but are expected to back it after the conclusion of second reading, its first Commons stage, late on Monday or in the early hours of Tuesday.
But they have warned they are ready to back amendments to the Bill at future stages, raising the prospect of the minority Government being bounced into concessions to avoid defeat in House of Commons votes.
The Bill overturns the 1972 Act which took Britain into the European Economic Community and incorporates relevant EU laws into the UK statute book to prevent black holes in the law at the point of Brexit.
The votes are likely to take place in the early hours of Tuesday morning.