MPs face a “stark” choice between a short delay to Brexit – if they back Theresa May’s deal – or a much longer one if they reject it, a minister said.
David Lidington – Mrs May’s second-in-command – was speaking ahead of a vote later on delaying the UK’s departure from the EU on 29 March.
The PM will make a third attempt to get MPs to back her deal in the next week.
If it fails again, Mr Lidington said MPs would get two weeks to decide what they wanted to do instead.
Voting is due to get under way at 17.00 GMT, with the vote on the main government motion expected at about 18.15 GMT.
Labour’s Shadow Brexit Secretary Sir Keir Starmer said: “The idea of bringing back the deal for a third time, without even the pretence that anything has changed, other than, of course, using up more time, is an act of desperation.”
He said a government motion simply calling for a delay to Brexit would be easily passed, but by “wrapping it up” with a third vote on her deal, the PM risked further “splits and divisions” in her own party, something he said was “absurd and irresponsible”.
US President Donald Trump has also weighed into the debate, saying Brexit is “tearing countries apart”.
“I’m surprised at how badly it has all gone from a stand point of negotiations but I gave the prime minister my ideas of how to negotiate it, she didn’t listen to that and that’s fine but it could have been negotiated in a different manner,” said Mr Trump.
He was speaking in the Oval Office after greeting Irish premier Leo Varadkar.
In July last year, Mrs May said Mr Trump had advised her to sue the EU rather than negotiate over Brexit.
In the Commons, David Lidington indicated that the government would allow MPs to hold a series of votes on possible ways forward on Brexit if MPs again rejected the PM’s deal.
But he warned that a longer extension would mean “a sustained period of uncertainty… which I fear would do real damage to the public’s faith in politics and faith in democracy”.
And it would also mean that the UK would have to contest the European Parliament elections in May, he added.
MPs will vote later on a motion calling for a three month delay to Brexit if MPs back Mrs May’s deal – or a longer one if MPs do not support it by 20 March, the day before the next EU summit.
Any length of extension has to be agreed by the EU.
European Council president Donald Tusk has indicated that the EU may be ready to offer a lengthy extension to negotiations if the UK wants to “rethink its Brexit strategy and build consensus around it”.
Northern Ireland’s Democratic Unionist Party – which twice rejected Mrs May’s deal in the Commons – earlier held talks with the government to see if a solution could be found allowing its MPs to support the PM in a future vote.
Commons Speaker John Bercow has selected a series of amendments to be voted on later.
These include a bid to allow Parliament to decide what kind of Brexit deal should be negotiated if talks with the EU are extended, in a series of “indicative votes”.
One of the MPs behind this amendment, Labour’s Stephen Kinnock, told BBC Radio 4’s The World at One Mr Lidington’s offer of votes if the PM’s deal is defeated may meet their requirements.
“It may possibly mean that we don’t have to move our amendment,” he added.
Mr Bercow sparked anger among Brexiteers by blocking debate on another amendment, signed by 127 MPs, which sought to rule out a second EU referendum, with some MPs accusing him of bias.
The Speaker selected a rival amendment calling for a second referendum, as well as another from Labour backbencher Chris Bryant challenging Mrs May’s plan to bring her EU deal back to the Commons for a third “meaningful vote”.
He told MPs they should “not conclude anything” about his views on Brexit from his decisions, adding that he always did his best to be fair.
The People’s Vote campaign said it did not support the amendment calling for another referendum tabled by Independent Group MP Sarah Wollaston.
“We do not think today is the right time to test the will of the House on the case for a new public vote,” said the spokesman.
“Instead, this is the time for Parliament to declare it wants an extension of Article 50 so that, after two-and-a-half years of vexed negotiations, our political leaders can finally decide on what Brexit means.”
Sir Keir Starmer indicated that Labour would not be backing Ms Wollaston’s amendment either, as it was not the right time.
Scotland’s First Minister Nicola Sturgeon, who supports another referendum, has, meanwhile, urged Mrs May to consider an alternative to “bullying” MPs into backing her proposals.
MPs voted on Wednesday evening to reject a no-deal Brexit under any circumstances.
No date has yet been set for the third so-called “meaningful vote”.
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