A section of Labour MPs are expected to defy the official party position and vote in favor of a Lords amendment to keep the United Kingdom in a Norway-style trading arrangement, better known as the European Economic Area (EEA), post-Brexit.
Corbyn instructed his MPs to abstain on the amendment, meaning they should neither vote for or against it.
Parliamentary debates about complex legal amendments rarely rouse much heat, but passions run high over anything to do with Brexit.
Anna Soubry, a pro-EU Conservative lawmaker, said she knew of one legislator who would not vote with their conscience because of "threats to their personal safety" and that of staff and family.
The vote on Tuesday is the first of two days of debate that will test May's authority and her plans for leaving the EU.
At the very least, the amendment places a requirement on the United Kingdom government to negotiate a deal with the European Union which closely mirrors current arrangements, if not replicating them in their entirety.
Another flashpoint could come when lawmakers vote Wednesday on an amendment seeking to keep Britain in a customs union with the EU.
The Prime Minister appears to have rowed back on promises to rebel MPs yesterday that she would discuss another concession with them this week.
"Anything that undermines the government at home will make negotiations with the European Union more hard", May told a meeting of her cabinet. The strength of this commitment is yet to be seen in writing - and the Brexit department is still insisting it has not given up control of the negotiations - but the anti-Brexit rebels showed they have the numbers to force a defeat should the government renege on its pledge.
Today the government avoided an embarrassing defeat on a key Brexit vote by offering concessions to Remainer Tory MPs.
During Commons exchanges, supporters of the EEA said it would be an economic "lifeboat" for the United Kingdom after Brexit by reducing the disruption to business.
The government was putting a combative spin on the concessions Tuesday evening: "The Brexit Secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and Government in negotiating worldwide treaties, and respecting the referendum result", a spokesperson for the Brexit department said in a statement.
You might never have heard of him, but Phillip Lee, a minister, has just resigned from his job in government in public over what he described as the government's "detrimental" Brexit policy.
As the vote approached, Tory MPs intending to defy the party whip in order to vote with Labour on the amendment left the chamber.
Talks with Brussels have stalled over the fraught issue of the Irish border, but both sides are hoping to agree a final deal by October in time for the break on March 29, 2019.
Prior to the vote, Labour's staunch pro-EU MPs - such as Chuka Umunna and Owen Smith - pleaded with the leadership to embrace the Norway option, as they believe it's the best chance retain full access to the single market.
It has been clear for a while that the now ex-minister, one of the rising generation in the Tory party, has been frustrated for some time.
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