Mrs May's Conservative Party only has a majority in Parliament with the support in key votes of the 10 MPs from Northern Ireland's Democratic Unionist Party, so any split raises questions about whether her plan could survive a Commons vote - and has also led to renewed questions about whether she will face a challenge to her position.
Ross Thomson, a prominent Leave campaigner in Scotland, condemned Mrs May's Chequers plan, which seeks to maintain close ties with the EU.
In his resignation letter, Foreign Secretary Boris Johnson warned the "Brexit dream was dying".
They have tabled for amendments to the Customs Bill on the eve of the government publishing a white paper setting out Theresa May's blueprint in full.
"We think it is possible to negotiate independent trade policies after we leave the European Union".
"What I found when I was talking to people on Saturday, I was out canvassing on Saturday, people like the fact that we are delivering on what they voted for". Does she rely on Labour votes to achieve Brexit or does she change her mind and go back to Lancaster House?
Mr Thomson said the Chequers plan would be the equivalent of being "in the customs union in all but name, in the single market in all but name, and essentially still under the jurisdiction" of the European Court of Justice.
Ross Thomson, who represents Aberdeen South, used a podcast for the Brexit Central website to criticise the plans agreed by Cabinet members at Chequers.
Mr Corbyn, whose own party is split on Brexit, says Mrs May should call a General Election if she can not win support for a final Brexit deal.
"But the resignation of Brexit Secretary David Davis, and some opportunist goal hanging by Boris Johnson, has cut exporters" celebrations short.
"I think if the prime minister makes further concessions with the European Union then there will no doubt be more resignations from Brexiteers in the Cabinet, from junior ministers to PPSs, because there is only so much that you can give in a negotiation", she told BBC2's Newsnight.
That is more than the 48 required to trigger a no-confidence vote in May, if unhappy MPs were to lodge a formal objection with the chair of the party's backbench 1922 committee.
Mr Davis has been replaced by former housing minister, lawyer and leaver Dominic Raab.
But leading Eurosceptic Bernard Jenkin played down the prospects of more walkouts from the administration.
Speaking at the North Atlantic Treaty Organisation summit in Brussels, Mrs May insisted that her Chequers deal delivered on the "red lines" which she set out in her Lancaster House speech past year.
Hard Brexiters have pledged to mount a campaign of guerrilla warfare against May's government in an attempt to disrupt the soft Brexit proposal unveiled at Chequers, in which she proposed that the United Kingdom would share a "common rule book" of standards on food and goods after Brexit.