After a week in which parliament forced the government to promise to come back with a "plan B" within days if May's deal is rejected, Mr Barclay said the risk of parliament acting in a way that frustrates Brexit had increased.
The Sunday Times reported that some lawmakers are planning to seize control of the legislative agenda from the government in an act that would allow Parliament to extend the Brexit deadline or even overturn the decision to leave the EU.
British opposition Labour Party leader Jeremy Corbyn said on Sunday that exiting the European Union without a deal would be "catastrophic" and he would prefer an agreement is reached than a second referendum held.
Labour is also facing calls to put forward a vote of no confidence in Mrs May and a general election could take place should the Government lose.
"I think parliament is very committed to try to stop no-deal, but I think we have to recognise that there is a deal on the table, it does broadly deliver the Brexit people voted for, and if we don't find a way to get this through, we are taking some very big risks".
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He also appeared to out at Labour over the continued confusion about what stance it would take on Brexit if it secured a snap general election.
He wrote: "It's clear that if our government and parliament are incapable of finding a way out of this mess, it should be taken out of the hands of the politicians and returned to the British people to take back control".
"If MPs who represent seats that voted 70% to leave say "sorry guys, we're still going to have freedom of movement", they will turn against the political mainstream". We can not - and must not - let you down.
Rejecting her proposed package, she said it "would be a catastrophic and unforgivable breach of trust in our democracy".
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"So my message to Parliament this weekend is simple: it is time to forget the games and do what is right for our country".
One of her predecessors, Sir John Major, called for Article 50 to be revoked as he warned it would be "morally reprehensible" to crash out without a deal.
But former Brexit Secretary Mr Davis said the amendment also allows Britain to "go back to the European Union with our best and final offer".
But he has insisted the United Kingdom should not afraid of a no-deal Brexit, despite forecasts from the Treasury and Bank of England warning that it could trigger an economic crisis worse than the 2008 financial crash.
Mrs May was boosted on Thursday by two Tory backbenchers - her former policy adviser George Freeman, and Trudy Harrison - indicating they will back her deal, as well as by a call from Japanese PM Shinzo Abe for the United Kingdom to avoid no-deal.
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He was in the team in 1992 when South Africa played its first game after being allowed back into global soccer. He won 58 caps for South Africa, helping them win the African Nations Cup on home soil in 1996.
"I am committed to getting the best outcome for this country, which is supporting the prime minister's deal".