"If, in the future, I am to look my children in the eye and honestly say that I did my best for them I can not, in all good conscience, support how our country's exit from the European Union looks set to be delivered".
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
MPs will spend a total of 12 hours debating and voting on 14 Lords amendments to the EU Withdrawal Bill - six hours on Tuesday and six hours on Wednesday.
Tory whips are pressing potential pro-EU rebels in the Conservative Party's ranks to make sure the party rallies enough votes to win.
The government still faces a knife-edge vote on how much power the Commons will have over the final Brexit deal.
A deal between the two factions was brokered last night, with Brexiteer Jacob Reed-Mogg and former minister Nicky Morgan putting their names to an amendment committing to a new "customs arrangement", replacing language on staying in the customs union.
Yet, the Labour camp is split on the Brexit issue between pro-Leave MPs ready to vote with the government, and rebels who've come out against their own party's amendment to support the country's membership in the European Economic Area.
Conservative MP Sarah Wollaston said on Monday morning she was "minded" to defy party orders and back the meaningful vote amendment.
Conservative Remainer MP Sarah Wollaston told BBC Radio 4's Today program that she was "minded" to defy the government on the first of these amendments, which calls for parliament to get a "meaningful vote" on any final deal agreed between the United Kingdom and EU.
The bill returns to the House of Commons with the PM hoping to overturn 15 amendments made by peers in the House of Lords.
Phillip Lee, a justice minister and personal friend of May, quit in a dramatic speech in central London in which he attacked "badly rushed" Brexit negotiations and insisted he could no longer serve in an administration pursuing a policy that failed in its duty to protect the public.
Mr Clarke had urged the rebels to hold their nerve.