Mr Buckland, who was a Remain supporter, was standing alongside junior Brexit minister and Leaver Steve Baker when he made the comments.
UKIP's General Secretary Paul Oakley said Tories who rebel this Tuesday would be "betraying Brexit" and urged them to stick to their promises to leave the EU.
Nigel Dodds from the party said: "I think they're absolutely critical, these are two of the most significant, important days since the Brexit referendum".
"The government's position isn't a position, its a sham to get through the next 48 hours and keep Jacob Rees-Mogg in check".
In a tweet this morning, he said, "I am incredibly sad to have had to announce my resignation as a minister in Her Majesty's Government so that I can better speak up for my constituents and country over how Brexit is now being delivered". I am confident I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible.
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"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
Some pro-EU Tories were reported to be backing away from voting against government, over fears that a defeat could prompt a leadership contest and see Mrs May replaced by a far more hard-line Brexiteer.
It's anticipated that May will tell her backbench rebel MPs on Monday evening that they need to unite behind the rest of their Tory colleagues and the government, as it is their duty "to deliver on Brexit".
On Tuesday, parliament will also debate other amendments, including a challenge to the government's plan to put March 29, 2019, or "Brexit Day", into law and an attempt to toughen a commitment to ensure a frictionless border between Northern Ireland and the neighboring Irish Republic, which will remain in the EU.
"We must be clear that we are united as a party in our determination to deliver on the decision made by the British people", she is expected to tell the backbench 1922 Committee.