The options that have so far gathered maximum support involve closer ties to the European Union and a second referendum.
Deputy chairman James Cleverly initially said the party was "not planning" for a snap general election to resolve the Brexit deadlock, but moments later admitted that the opposite was the case. The date was postponed to allow Mrs May more time to find a Brexit solution.
Mr Gauke explicitly blamed Tory rebels, telling Marr Britain was in this situation because "too many colleagues" were not backing the deal.
He also raised the future of Northern Ireland under such a scenario. Once it is apparent there's going to be a leadership election and one of them might become prime minister, the question of a vassal state disappears and they support it.
MPs will hold another set of non-binding votes on various Brexit options in the Commons on Monday. A customs union with the EU is thought to be the most likely preference.
A no-deal Brexit is a serious threat to the UK.
Justice secretary David Gauke told the BBC that the government will have to consider "very carefully the will of parliament".
Lewis said, however, that seeking a customs union with the EU would be hard and would go against the result of the referendum and Conservative pledges before the 2017 national election.
And if it doesn't pass at this fourth attempt, well then we are into mega crisis territory because at that juncture the PM would be mandated by MPs to negotiate with the EU a customs-union-based Brexit.
"I fear we are reaching the limits of this process in this house", she said.
She told Today: "There have been periods in our history when we have had national unity governments or a coalition for a very specific issue".
A large pro-Brexit demonstration in the United Kingdom capital erupted Friday following the third defeat of May's withdrawal deal in the parliament. Currently, Brexit is due to take place at 2200 GMT on April 12 unless May comes up with another option.
"The House has been clear this deal now has to change", he said.
"We need to stick to this task that we have in relation to the European Union", he said.
Former British Prime Minister John Major has urged Theresa May not to call a general election in the coming weeks.
He said he suspects MPs may add "something relating to the customs union and alignment to the single market" to May's deal, noting: "If they add that to her deal, it's not flawless, it's far from ideal".
But Downing Street later said this was not an "inevitability".
It is therefore expected that Mrs May will try to secure a much longer Brexit delay at an emergency summit of the European Council on April 10th if Meaningful Vote 4, or MV4, is a non-starter - with reports indicating she will seek to put Brexit off by nine months.
The federal government is warning Canadians in the U.K.to "exercise a high degree of caution" as Brexit protests intensify in London after a third "no deal" vote.
Data from the last three votes may shed some light.