She noted that lawmakers will be able to amend her plan when it comes to a vote in the House of Commons on 29 January exactly two months before Britain is due to leave the EU.
The bloc awaits new ideas from London, after the British parliament struck down the Brexit deal Prime Minister Theresa May had negotiated with the EU.
Labour leader Jeremy Corbyn said the amendment was created to "break the deadlock" and rule out a "disastrous" no-deal Brexit.
Phillipson, the MP for Houghton and Sunderland South, said she "disagreed with a lot of what Jo says" but that securing a second referendum "will involve working with people I disagree with on other issues".
The former Cabinet minister said a second vote would inevitable produce only a narrow victory for either side, but was coming "unless some extraordinary turn of events prevents it", adding: "It's coming by a process of elimination, not because it's a good idea in itself".
She also repeated arguments against a second referendum - another "people's vote" on Brexit.
Aided by the flamboyant speaker of the House of Commons, John Bercow, backbenchers and opposition members of Parliament have been successful in passing arcane procedural amendments that may give them more say - and more meaningful votes - on the ultimate Brexit deal.
The two Labour MPs were speaking alongside Swinson and the Green party's Westminster leader, Caroline Lucas, at the launch of a pamphlet criticising Labour's principal Brexit plan as well as the no-deal and "Norway plus" alternatives.
DUP leader Arlene Foster urged Mrs May to return to European Union leaders and renegotiate to secure a "better deal".
Argentine soccer player Emiliano Sala aboard missing plane
Conditions were treacherous during the search with rough seas, heavy rain and gusts forecast to reach up to gale-force eight. A journalist from Ouest France tweeted to say Sala had been on the plane - but there has been no confirmation.
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The letter by a wide array of China experts from around the world is addressed to Chinese President Xi Jinping. Two former USA ambassadors to China, Gary Locke and Winston Lord, also signed.
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"Sarri has probably thought he's an experienced guy, he's been around the block, and thinks he doesn't need to take it". A capitulation at Arsenal was the moment for Maurizio Sarri to unload pent-up frustration with his Chelsea squad .
The move came is it was understood that Work and Pensions Secretary Amber Rudd had urged Downing Street to allow Tory MPs a free vote on moves aimed at preventing a no deal, amid fears that dozens of ministers could otherwise resign.
It came as Theresa May was due to hold her weekly Cabinet meeting to discuss her next moves, with backbenchers also planning various amendments created to make various changes on Tuesday.
She said any of the alternative deals being pushed would still require "the insurance policy": "No backstop simply means no deal now and for the foreseeable future".
"It's clear already that a significant number of colleagues have expressed concerns about the backstop and that's one of the areas we're going to be looking at", her spokesman said ahead of a statement by May to MPs later on Monday.
"We still need clarity on Labour's position in a public vote and whether, as members want, we would campaign robustly for our continued membership of the European Union".
In a nod to the European Union, she offered to waive a settled status fee for European Union citizens living in Britan.
The Great Grimsby MP tweeted: "This may mean that I am required to step down from my front bench housing role if it is a whipped vote".
"Parliament has not got the right to hijack the Brexit process. and in fact steal the result from the people", he told BBC television.
Several MPs pointed out that far-right protestors have targeted referendum-supporting Tories like Anna Soubry recently, accusing them of being traitors.
Labour's Hilary Benn, chairman of the Brexit Select Committee, tabled an amendment calling for a range of indicative votes on various Brexit options.