Tory leadership contender Mark Harper has said it is "not going to be possible" to leave the EU on October 31, as he made his pitch to be the next prime minister.
The former immigration minister admitted he might upset some in his party by not promising to deliver Brexit by the current Article 50 deadline.
But at his official campaign launch he said: "It is not credible to say you can renegotiate the Withdrawal Agreement and get it through both Houses of Parliament by October 31."
Mr Harper sought to play up his working class credentials in a session where he invited journalists to "ask him anything", and admitted he was the outsider in the race to replace Theresa May, calling himself a "serious underdog".
On Brexit he said he was the only candidate with a "realistic and credible" plan, adding he was "comfortable leaving without a deal", but said it is "better to have a deal".
He added that he didn't "think you can credibly say you've done everything humanly possible to get a deal" by the end of October, saying at that point there would not be a majority in Parliament to allow a no-deal.
And he dismissed the idea of proroguing Parliament, saying it would "test our constitution to destruction", adding he did not want to "drag the monarch into the issue" and endanger the union.
But he did say the UK would have to be out of the EU by May 2020's local elections, because: "We're not going back to the country in any set of elections before we've left."
And he suggested he would consider a no-deal Brexit at that point if no changes to the Withdrawal Agreement were forthcoming from Brussels.
"If we approach our European Union partners in a spirit of openness, and we bust a gut, we do everything we can to get a deal, and they are simply not prepared to budge, then in those circumstances, and only in those circumstances, do I think there will be a majority in the House of Commons to leave without a deal," he added.
Criticising his rivals as all having been "sat around the Cabinet table and participated in decisions that have led to not leaving the European Union three years after the referendum", Mr Harper said he would offer a "fresh approach".
He said there was a "very narrow landing zone" to get an improved deal, but it would require earning "credibility with the Irish government" to fix the back-stop and border issue.
Criticising some other leadership hopefuls such as Esther McVey, who has said she will not renegotiate with the EU and look to force a no-deal, he said "rushing headlong to October 31 is not a credible plan".
And in a swipe at the frontrunner Boris Johnson and another high-profile contender Michael Gove, who have both promised to cut taxes, he said it was not right to "promise more money to higher rate taxpayers".
He said he wanted to put more money into education, further education and apprenticeships, but he was "not going to be plucking figures out of the air and making commitments" at this early stage.
Mr Harper, 49, who was chief whip under David Cameron from 2015 to 2016, also said he would assemble a Cabinet "that doesn't leak like a sieve", and instil "proper discipline" and a "functioning Whips Office" if he got the top job.
He dismissed the idea his campaign, which at 200/1 has the longest odds of any of the 10 candidates, was simply an attempt to get a Cabinet role with the eventual winner.
He said there are "easier ways of getting a job" than running to be prime minister, and he was standing: "Because I have the skills to get the job done."
He said he "knows how to beat the Labour party and keep them beat" having won his seat from them in 2010, and vowed to "see this contest the distance", adding: "Whatever job they offer me, I'm not going away."
Mr Harper also defended the controversial "go home vans" sent out by the Home Office to deter illegal immigrants, which he signed off as immigration minister in 2013.
He said they had piloted a number of measures, adding the vans were "not successful and we didn't do it again", but said he did not "resile from the message" they carried.
The final question he was asked was more light-hearted, with the MP for the Forest of Dean asked: "Who would win in a fight, a lion or a bear?"
He replied: "On the basis that the lion is the symbol of Britain, I'm going to say the lion."