The British government is holding talks with Northern Ireland's Democratic Unionist Party, which has strongly opposed the Brexit divorce deal.
"I hope that MPs (lawmakers) of all parties will be over this weekend reflecting on the way forward", Lidington told BBC radio, adding the legal default was still that Britain would leave on March 29, unless something else is agreed. Much will depend upon the position of hard-line Brexiteers and the DUP, as they calculate whether it is better to fall in line behind the prime minister, or face a potentially lengthy Article 50 extension that might last until at least 2020 and risk Brexit being jeopardized by a second referendum.
"You don't just have a short, technical extension to our membership of the European Union, you nearly certainly need a significantly longer one to find a time for parliament to come to a majority verdict", he told BBC radio. However, more than half the total number of MPs voted against the motion, making clear the lack of support in the House of Commons for staging a second vote.
This so-called Norway option means Britain would have to accept most of Brussels rules with no say over their formulation along with continued free movement.
"There's so much that we can achieve outside the European Union and it is time we got into the position where we can start to focus on that". All 27 leaders must unanimously agree.
However if they reject her deal again then she says she will seek a longer extension - but any delay has to be agreed by the 27 other European Union member states.
Pelosi is right: Dems can't impeach Trump. She should explain that honestly
He declined to say when he plans to take action, saying, "The acid test is one that does not carry with it a specific date". House Speaker Nancy Pelosi has ruled out impeaching US President Donald Trump , saying "he's just not worth it ".
The Government won the vote on giving Parliament the opportunity to choose another Brexit approach by just two votes, with 16 Tories rebelling against their party.
Negotiation of a new deal "would mean a much longer extension - nearly certainly requiring the United Kingdom to participate in the European Parliament elections in May", she told The Sunday Telegraph.
However, despite pushing for another referendum, the People's Vote campaign have decided that this is not the right time.
But closer to home he said he hoped his discussions with Mr Tusk could help avoid a "rolling extension".
A spokesman for the European Commission said extending Article 50, the mechanism taking the United Kingdom out of the EU on 29 March, would need the "unanimous agreement" of all EU member states.
Former cabinet minister Owen Paterson said: "We will fight this to the very end".
Opposition and backbench MPs are still on the backfoot in this process and need the government to decide on the forthcoming parliamentary business, or next steps.