By James Masters, CNN

(CNN) -- Britain's embattled Prime Minister Theresa May has warned that a failure by lawmakers to back her Brexit deal risks the entire venture being canceled.

May has come under fire from huge sections of her own Conservative Party over her deal and is facing a revolt ahead of Tuesday's scheduled vote on her deal in the House of Commons.

But speaking to the Mail on Sunday, May insisted that if members of her own party were to rebel, it would leave the country in "uncharted waters."

"If you want Brexit, make sure you get it, and that's about this deal," she said.

"When I say if this deal does not pass we would truly be in uncharted waters, I hope people understand that this is what I genuinely believe and fear could happen. It would mean grave uncertainty for the nation with a very real risk of no Brexit or leaving the European Union with no deal."

May also rejected the growing clamor for a second referendum, or "People's Vote" which a number of lawmakers have called for in the absence of a deal.

"We had a people's vote, that's what frustrates me when people talk about this, the second referendum being a people's vote, " she added.

"We had a people's vote, let's deliver on the first people's vote."

May's comments came as thousands of pro-Brexit protesters took to the streets of central London on Sunday to march against the Brexit deal, which protesters labeled a 'Brexit Betrayal,' and call for a complete withdrawal from the European Union.

The protest was organized by the UK Independence Party (UKIP) and anti-Islam activist Tommy Robinson. Robinson, whose real name is Stephen Yaxley-Lennon, has become a figurehead for the far right in Britain and is currently an adviser to UKIP leader Gerard Batten.

In response, thousands of anti-racism campaigners and Labour-backed groups staged a counter protest on the same day under the banner "Stand Up to Racism." Demonstrators expressed concern about what they say is the growth of the far right in the country.

May is facing pressure from some sections of her party over her deal, particularly the backstop arrangement for the Northern Ireland border.

Tuesday's vote is likely to be tense, with Labour, Liberal Democrats, Scottish National Party and Northern Ireland's Democratic Nationalist Party, which has propped up the government since the general election in June 2017, all set to vote against the deal.

Speaking on Sky News' Sophy Ridge on Sunday, Conservative lawmaker Esther McVey, who quit the Cabinet over the Brexit deal last month, warned that defeat for May would mean she should "immediately" return to the European Union to "get a better deal" if she loses in the Commons.

She cited the backstop to the Northern Ireland border should be removed, a deal that Boris Johnson, the former foreign secretary, claims will leave the UK open to "blackmail."

"The real problem with the backstop arrangement is it gives the power to Brussels and to all the other EU member states effectively to blackmail us and to get what they want out of the future trade negotiation," he told the BBC's Andrew Marr Show. "It is a diabolical negotiating position."

The government's perilous position has led to speculation that Tuesday's vote may be rescheduled with May reportedly struggling for numbers.

But Steve Barclay, her third Brexit Secretary, insists the vote will go ahead as planned.

"The vote is going ahead," he told the BBC.

"That's because it is a good deal, it's the only deal and it's important we don't let the perfect be the enemy of the good."