Any changes to the bill will return to the elected House of Commons for debate, likely in May, when pro-European members of the ruling Conservative party will have to decide whether to make a stand. On the other hand, she has hardcore pro-Brexit Tory MPs, according to The Times, warning that a vote of no confidence could be on the horizon if she reneges on her promise to leave the customs union.
Reports are suggesting that Theresa May could be willing to U-turn on the Customs Union.
Lawmakers will have to decide whether to back the government or reject the agreement - with the risk that Britain could crash out of the European Union next year without any deal in place. Whether Britain should stay in the customs union or leave it to strike a trade deal from outside the bloc will be part of the Brexit Trade Bill, which will be voted upon in May. The newspaper reported that May's office believed Fox and Johnson would quit rather than accept staying in the European Union customs arrangement, but that other euroskeptics such as Gove would remain.
The Irish border is a key element of their case.
Brexiteers fear the parliamentary arithmetic, combined with Brussels's rejection of Britain's customs proposals and the need to show how a hard border can be avoided, will push the prime minister into seeking some kind of customs union with the EU.
They have forced themselves into a trilemma in which it has adopted three positions, only two of which can be achieved at any one time - to avoid a hard border within the island of Ireland, for the United Kingdom as whole to leave both the customs union and the single market, and to rule out any special arrangements for Northern Ireland in relation to a customs union and single market.
Critics also argue that the much-heralded benefits of free trade deals with the likes of the USA and Australia would not be felt immediately as it would take years to reach an agreement.
Speaking on Monday, she remained strong on her stance.
"This is a welcome decision by the House of Lords". After all, this would be a huge gamble given we are in a hung parliament.
The vote can be overturned by the lower house, the House of Commons, but shows the deep divisions over Brexit across the Houses of Parliament and could encourage lawmakers hoping to derail her plans.