Ministers want to overturn or alter 14 out of 15 amendments to the bill proposed by the House of Lords in mid-May.
The amendments are designed to keep the UK closer to the EU after Brexit.
Ahead of the “marathon” debate, set to last more than 12 hours on Tuesday into Wednesday, the prime minister will remind pro-EU Tory MPs they have a duty to deliver on the referendum vote to leave the EU.
During what is likely to be a highly-charged appearance before the backbench Conservative 1922 Committee on Monday evening, Mrs May will highlight that although the bill is largely a technical measure, the way her party votes will send an important signal to the country.
“The purpose 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.
“But the message we send to the country through our votes this week is important. We must be clear that we are united as a party in our determination to deliver on the decision made by the British people.
“They want us to deliver on Brexit and build a brighter future for Britain as we take back control of our money, our laws and our borders.”
Despite only holding a Commons majority thanks to 10 DUP MPs, there were signs of cautious optimism among ministers they would get the votes to hold off a revolt.
The prime minister’s spokesman on Monday said the Brexit Bill is a “vital piece of legislation” and “with that in mind we would urge lawmakers to support the government”.
Amid fears Mrs May’s tenureship could be at risk from a defeat, some pro-EU Tories are reportedly backing away from a rebellion.
But ministers are taking nothing for granted, with whips working hard over the weekend to convince MPs.
They were working against veteran former chancellor Kenneth Clarke who urged rebels to hold their nerve, saying that if they succeeded they would strengthen Mrs May’s hand against the Cabinet’s Brexit hardliners.
He dismissed claims a government defeat could lead to a general election where Jeremy Corbyn could take power.
“Nobody in the House of Commons wants a general election. Most Labour MPs are as terrified of the idea of a Corbyn government as I am,” he told the BBC One Sunday Politics programme.
“What we need to do is to rescue the Prime Minister from this terrible treatment she is getting from key members of her Cabinet.”
There are two amendments which the government is thought to be most vulnerable on.
One is on the customs union, which would prevent the UK leaving the EU until the government lays out details of negotiations of the UK’s participation in the customs union by 31 October 2018.
The other would give Parliament a decisive say over what happens next if it rejects a final Brexit deal.
There were signs not all Tory MPs will play ball after Remainer Sarah Wollaston said on Monday morning she was “minded” to rebel over voting against the Lord’s amendment which forces the government to make remaining in the European Economic Area a negotiating objective.
However, she said all Conservative MPs would support the prime minister if there was a vote of confidence.