Another, Andrea Jenkyns, said she would now definitely vote against the deal and urged colleagues in the European Research Group (ERG) of Tory Eurosceptics to "hold our nerve".
Theresa May said she had achieved "legally binding" changes to her Brexit deal which addressed the possibility of the temporary divorce arrangement known as the "backstop" becoming permanent if the United Kingdom wished to end it.
It is likely to turn wavering Tory Brexiteers, who had been awaiting Cox's judgment on the concessions, back against May's deal in large numbers.
The back-stop measure is meant to reassure Britain it won't be trapped forever in a mechanism created to prevent a hard border between Ireland and Northern Ireland.
However, he said the situation was unchanged if a deal that supersedes the backstop can not be reached "through no such demonstrable failure of either party".More news: Ex-British soldier to be charged in Bloody Sunday murders
The pound sterling has soared to its highest figure in almost two years after Prime Minister Theresa May struck a Brexit breakthrough.
She claims the changes now means the Irish backstop - the insurance policy created to avoid a hard border in Ireland - could not "become permanent".
"It will consider facilitations and technologies - both those now ready and emerging".
Ms May had hoped that revisions to a Brexit deal over the Irish backstop, or protocol, secured late on Monday would offer enough assurances to get her deal through parliament.
Most observers see it as highly unlikely the deal will pass through parliament and Mrs May's spokesperson has been forced to deny rumours the prime minister may delay the vote with only a couple of weeks to go until the United Kingdom leaves the EU.More news: UnitedHealthcare expands program to pass drug discounts on to consumers
Cabinet office minister David Lidington told the House of Commons on Monday night that the two sides agreed on a "joint instrument" clarifying the withdrawal deal.
She would have looked first to the Democratic Unionist Party of Northern Ireland, whose 10 votes give her minority government a theoretical majority - and whose implacable opposition to the Northern Irish "backstop" in her deal has put down a marker for May's other Conservative foes and prompted the weeks of shuttle diplomacy with Brussels.
"We note the prime minister's latest statement and update on our European Union exit negotiations", it said. We will be taking appropriate advice, scrutinising the text line by line and forming our own judgement. These publications need careful analysis.
"We will measure this latest text against the Brady amendment and the commitments made by the prime minister on 29 January".More news: Brazil police: 2 men arrested in killing of Marielle Franco