The prime minister emerged to give a speech in Downing Street after five hours of discussions she described as "impassioned".
During the cabinet meeting, British journalists said anger among Brexit-supporting Conservative MPs was so high that they might call for a vote of no confidence in her leadership.
May's critics say this will keep the country in a potentially open-ended customs union with the EU.
One of the chief obstacles ahead for May if she is going to get her Brexit agreement through could be the House of Commons, where a simple majority of MPs will need to vote for the blueprint for the deal to be given the green light.
Earlier, May told lawmakers in the House of Commons that the draft deal "takes us significantly closer to delivering what the British people voted for in the referendum" of 2016 that opted to leave the EU.
Some key pro-Brexit ministers, including worldwide development secretary Penny Mordaunt and work and pensions secretary Esther McVey, were named as possible members of her Cabinet who might resign in protest and possibly even pave the way for a leadership challenge against the PM.
The ultimate outcome for the United Kingdom remains uncertain: scenarios range from a calm divorce to rejection of May's deal, potentially sinking her premiership and leaving the bloc with no agreement, or another referendum.
One key issue has set these pro-Brexit ministers at odds with May: the plan for avoiding customs checks at the border between Ireland and Northern Ireland.
The solution is meant to be temporary, but pro-Brexit politicians in Britain fear it may become permanent, hampering Britain's ability to strike new trade deals around the world.
The outline political declaration - which will be subject to further negotiation over the coming weeks - expresses an ambition to achieve zero tariffs and no quotas in EU-UK trade, something the officials said no other major economy had achieved. During this period nothing will change, and businesses can carry on operating as now.
He added that a special North "backstop" would only be used if the two sides fail to reach a broader agreement within a 21-month transition.
It commits the United Kingdom to protecting "North-south co-operation and its guarantee of avoiding a hard Border, including any physical infrastructure or related checks and controls, and bearing in mind that any future arrangements must be compatible with these overarching requirements".
Under backstop arrangements created to keep the Irish border open, if no trade deal is agreed by the end of the transition period in December 2020, a temporary "EU-UK single customs territory" would be established.
"There comes a point at which the individual and the policy are so inextricably interlinked that that argument ceases to have any validity", according to Rees-Mogg.
British Prime Minister Theresa May won the backing of her senior ministers for a draft European Union divorce deal on Wednesday, freeing her to tackle the much more perilous struggle of getting parliament to approve the agreement.
The Parliament website lists 93 MPs who are ministers and would therefore be bound to support Theresa May's Brexit plans owing to collective responsibility.
Speaking outside Number 10, the Prime Minister said: "I firmly believe that the draft withdrawal agreement was the best that could be negotiated and it was for the Cabinet to decide whether to move on in the talks". However, the accord still needs to be approved by the United Kingdom lawmakers and the EU Parliament. Brexit supporters in May's party, which has been riven by a schism over Europe for three decades, said she had surrendered to the European Union and that they would vote down the deal.