Jacob Rees-Mogg is the chairman of the influential European Research Group of backbench Tory Brexiteers.
Finance minister Hammond sparked a row on Thursday when he spelled out his hopes for Brexit, prompting a backlash from eurosceptics who forced him to clarify that he still backed the country's withdrawal from the EU single market and customs union.
The intervention, in a speech in Middlesbrough, comes after Mr Davis clashed with prominent Tory Eurosceptic Jacob Rees-Mogg over the terms of the transition period which the influential backbencher claimed will leave the United Kingdom a "vassal state".
Negotiations are likely to focus on the complexities of that status quo, including giving Britain a non-voting seat at some EU meetings, how to determine current matters like annual fishing quotas and how the EU might allow London to sign up to new trade deals with other countries while bound by EU accords.
Rees-Mogg said that Britain would be a "vassal state" during the transition as it would continue to pay into the EU budget and remain subject to the jurisdiction of the European Court of Justice.
"Then what will be the point of voting for the party that's implemented it". I'm really keen to see a Labour government because there are many things to be done, not least pursuing a sensible Brexit and not one that damages our economy and jobs.
It states that the "full competences" of the European Union institutions - "in particular" the ECJ - should be preserved during the transition period, which should not run beyond December 31 2020 - 21 months after Britain formally leaves the bloc.
More than 2,500 people - business leaders, politicians such as Donald Trump, diplomats and the odd celebrity, such as Cate Blanchett - will fly in for the 48th annual Davos meeting.
France has stepped up efforts to attract London banks preparing for Brexit to Paris after the election of President Emmanuel Macron, who has begun to make more flexible labor laws and tax cuts.
Tory disquiet over Theresa May's leadership appears to be growing.
Many wonder whether lawmakers may soon trigger a motion of no-confidence: 48 MPs must submit letters to the chairman of the 1922 Committee of backbenchers to force the vote.
It goes without saying, of course, that the Goves, the Rees-Moggs and the Johnsons of this world would not be playing these risky, chauvinistic games with our economic future if their own friends and families stood to lose their livelihoods and financial security because of it; but that's how it rolls, when voters mistake a bunch of privileged nostalgists and wealthy mischief-makers for friends of the people.
He said: "There is a lot of jealousy about Boris because he is an enormously popular figure".
"However, during the transitional period, the Government must put jobs first and aim to secure a Brexit deal that prioritises the working people of this country".
Reports have also suggested that MPs believe Defence Secretary Gavin Williamson is positioning himself for a leadership bid.
"This means we must discuss how regulators and agencies can best provide continuity and clarity for businesses during this period in a way that benefits everyone".
A spokesman said: "This is a categoric lie".
"And we agree on the need to base this period on the existing structure of rules and regulations", he said.