Since May's deal was rejected in the Commons on 15 January by 432 votes to 202, opposition and backbench MPs have been tabling amendments to the plans.
"The prime minister is committed to leaving the European Union with a deal, but clearly if we are to obtain parliamentary support for that deal some changes are going to have to be made", the spokesman said.
"The backstop is not a prerequisite for the future relationship", she said.
Parliament will vote on proposed changes to May's beleaguered Brexit plan from 7 p.m. London time, with Speaker John Bercow choosing which amendments get picked.
Another notable one is much softer and non-binding in nature.
Amendment I: Spelman (Conservative) and Dromey (Labour) - Attempts to prevent a no-deal Brexit by adding to the PM's motion that Parliament rejects a no-deal.
The two key proposals here are from Tory backbenchers, Andrew Murrison and Graham Brady, chair of the influential 1922 Committee, responsible for hiring and firing Conservative leaders.
Britain is reportedly making plans to declare a "state of emergency" and introduce martial law in the event of disorder breaking out following a No Deal Brexit.
The backstop would keep the United Kingdom in a customs union with the EU in order to remove the need for checks along the border between the UK's Northern Ireland and EU member Ireland after Britain leaves the bloc.
Hardline pro-Brexit Conservative MPs on Tuesday made clear their support for May depended on her securing a deal they approved of.
Moreover, Cooper's amendment would not identify a consensus among MPs to halt a no-deal Brexit.
Amendment: This cross-party effort, by Labour lawmaker Yvette Cooper and Conservative politician Nick Boles, would set a time limit beyond which the prime minister would have to ask for an Article 50 extension until the end of the year if no agreement has been struck. Downing Street said today the deal had to "change" if it were ever to be agreed by MPs.
David Phinnemore, professor of European Politics at Queen's University Belfast, said: "If it does go through, then clearly, it is being seen by some MPs as a way of getting support for May's withdrawal agreement, and it also gives the prime minister a sense of what she needs to get from the EU". He didn't name the exact date, but the Sky News sources claim it may happen on February 13.
The Brady and Cooper amendment have garnered the most attention in the run up to the vote, with the latter, if successful would force the PM to delay Brexit by 9-months.
British MPs have instructed Prime Minister Theresa May to reopen a Brexit treaty with the European Union to replace a controversial Irish border arrangement - and promptly received a flat rejection from Brussels. The EU, however, insists that it has no intention of changing the terms of last year's accord with London in any significant way.
A top European Commission official says it would be "a stupid thing" for the European Union to make any concessions to Britain that would put the bloc at a disadvantage just to clinch a Brexit agreement.
Lawmakers voted on seven Brexit proposals Tuesday, including the border change supported by May and several measures that seek to rule out a "no-deal" Brexit.
"That comes as no surprise to us at all, but what remains very concerning is that the Government here continues to look away from that reality".
On Tuesday, lawmakers will debate and vote on May's next steps, with some hoping to gauge the level of support for alternatives to her deal and others even seeking to wrestle control of the process from government.
Or does she tie herself to the mast of Morgan/Baker, knowing it is the route to a no-deal Brexit and the probable collapse of her government?