"These next seven days are going to be critical, they are about the future of this country", May told Sky News.
Altmaier said: "I am sure that if one side undoes this package, other sides also will probably try to undo it".
They are aiming for 48 letters of no confidence, the number needed for a vote under Conservative Party rules.
More than 20 have publicly said they have done so.
The confidence vote now appears to be on hold until after Parliament votes next month on Mrs May's Brexit deal, which will itself be seen as a referendum on her leadership.
Speaking at a press conference this morning, Barnier said the draft Brexit deal reached between the bloc and London was "fair and balanced" but admitted an extension to the transition period was possible.
'I do think there is a point at which, we probably should have done it before, where we just say "I'm sorry, this is the United Kingdom of Great Britain and Northern Ireland, we can not accept those dictated terms"'.
"Politics is a tough business and I've been in it for a long time", she said during an television interview on Sunday, adding that the next seven days "are going to be critical" for the future of the United Kingdom and that she will be travelling to Brussels to meet with EU leaders before an emergency European Council summit on November 25.
"If the unacceptable deal goes through - and I never predict these things - there will be substantial economic damage and then I'm happy to say we will have to say to the people of Scotland "make your choice".
Aston Martin DBX SUV goes testing
After making its world debut three years ago as a concept vehicle , the all-new DBX is now closer to becoming a reality. It's going to go up some of the world's harshest environments - from the Arctic to the deserts of the Middle East.
The Brussels negotiations will finalise a parallel political declaration setting out a road-map for post-Brexit negotiations on future EU-UK ties.
The pro-Brexit ERG group of Conservative members of parliament published its assessment of the deal on Sunday, saying it would leave Britain "half in and half out" of the EU.
CBI president John Allan is expected to call for MPs to back Mrs May's deal - despite it not being "perfect" - and warn of the consequences of crashing of the European Union for businesses and the economy.
Mr Barnier said the European Union still needed to agree its own internal processes for triggering an extended transition period but insisted the focus this week was on the future framework talks. We don't believe it serves the interest of this country, therefore the Government have to go back to the European Union and renegotiate rapidly.
"Actually, the more I think about it, the more offensive "jump the queue" is as a description of a reciprocal right of free movement". "The biggest risk of no deal is taking a bad deal to the House of Commons.it is very important to take the action now".
Labour will vote down the deal in Parliament, Corbyn said, and he argued that a general election is now the "only sensible course of action".
Mordaunt, Raab, and five other top Conservatives - former foreign secretary Boris Johnson, Raab's predecessor David Davis, interior minister Sajid Javid, foreign secretary Jeremy Hunt, and Work and pensions minister Amber Rudd - are all "actively preparing" leadership campaigns, the Sunday Times said. "That is also the best way to build a good relationship in the future", Blumel said.
Asked about calls for a second referendum Mr Corbyn said: "It's an option for the future but it's not an option for today, if there was a referendum tomorrow what's it going to be on, what's the question going to be?"