International Trade Secretary Liam Fox said Labour's proposals were "not workable" while Boris Johnson accused Mr Corbyn of trying to trap the Government in a "toxic" Brexit.
May wants to win over lawmakers in her Conservative Party with changes relating to the Northern Irish border, but the EU has refused to reopen that part of the deal and instead wants May to pursue a compromise with the main opposition Labour Party by agreeing closer UK-EU ties.
European Union leaders stuck to their guns on Wednesday (30 January), insisting that the Brexit Withdrawal agreement rejected by UK MPs would not be renegotiated.
The Prime Minister's official spokesman said it would give MPs more time to "digest the content" ahead of a series of expected Commons votes on Thursday.
The prime minister struck a conciliatory tone in her response overnight and said she looked forward to the two parties meeting again "as soon as possible" to discuss ways forward on Brexit.
Mrs Leadsom said there was "no chance" Mrs May would adopt Mr Corbyn's "view of the world", adding: "The Prime Minister has been absolutely clear we're leaving the EU, we're leaving the customs union, we're leaving the single market".
They have also signed a deal to preserve the rights of some 43,000 British nationals living in Switzerland and the 35,000 Swiss residing in Britain after Brexit. The intervention came as the PM (pictured left returning to No10 today) moved to quell Tory fears that she is about to cave into Jeremy Corbyn's (pictured right) demand for a permanent customs union with the EU.
Thai king calls sister's bid to run for prime minister 'inappropriate'
Prime Minister Prayuth Chan-ocha, the preferred candidate of the military, is considered to be indelibly loyal to the monarchy. But the couple eventually divorced and she moved back to Thailand where she is still considered part of the royal family.
"I think that you would need to have a time limit".
"I think that gives that sense of timetable, clarity and goal on what we are doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that Parliament very firmly has", he said on BBC's Andrew Marr Show.
Theresa May is due to update the Commons later on the latest developments in negotiations with Brussels and Dublin, as the sides try to find a way through the impasse on measures for the Irish border.
His comments were echoed by former Conservative chairman Grant Shapps who tweeted: "No point winning Labour MPs, by losing Tories!"
Mrs May said securing frictionless trade for goods was "one of our key negotiating objectives". Although lawmakers asked for the backstop to be removed, May has said since that the backstop will remain, and that Parliament merely asked for it to be altered.
Speaking after a dinner with Brexit Secretary Steve Barclay on Monday night, European Union negotiator Michel Barnier said the talks had been "constructive", but added it was "clear from our side we're not going to reopen the withdrawal agreement, but we will continue our discussions in the coming days".
Labour's Brexit policy chief Keir Starmer told the Sunday Times newspaper that his party would seek to use the debate in parliament this week to prevent May from waiting until the last minute to come back with a deal, and compel her to present a fresh accord for lawmakers to consider before February 26.