"Some of you put your trust in the political process for the first time in decades".
And he warned of a "growing risk" that Parliament could frustrate Brexit, following reports of a plot to change Commons rules to enable backbench motions to take precedence over Government business if Mrs May's deal falls.
"Doing so would be a catastrophic and unforgivable breach of trust in our democracy".
The PM has also faced further opposition to her deal from former Brexit secretary Dominic Raab, who used an article in the Sunday Telegraph to urge MPs to vote down Mrs May's "bad" deal and send a message to Brussels that the United Kingdom "will not be bullied".
"So my message to Parliament this weekend is simple: It is time to forget the games and do what is right for our country".More news: NYC Mayor Proposes Mandatory Vacation Time For Workers
More news: Drip, Drip, Drip: Ex-Sanders Staffer Accuses Top Aide Of Sexual Assault
More news: Nokia 8.1 Plus renders reveal another phone with a hole-punch notch
Mr Grayling also said: "I have not asked for military support for the operations in Kent - that will be handled by Highways England and Kent Police".
Combating project fear tactics by soft-Brexit and Remain supporting MPs that clean-break Brexit can somehow be stopped, Tory lawmaker Anne-Marie Trevelyan told Sophy Ridge on Sky News Sunday that "the reality is the statute in place at the moment is to leave on the 29th of March either with an agreed deal, which the prime minister has been negotiating, or if one can't be reached by then on a no-deal basis and then we continue the conversation afterwards".
Mrs May also came under pressure from her former Brexit secretary Dominic Raab who told MPs to vote against her deal to show Brussels that the United Kingdom would "not be bullied". Every single household - rich or poor - would be worse off for many years to come.
"If it means that at a general election I lose my seat because of it, that's fine".
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'.
He rejected the idea that one of Labour's "six tests" for Brexit - that a deal should replicate the benefits of membership - went against the EU's basic tenets.
Blocking Brexit could lead to a surge in far-right extremism in the United Kingdom, the transport secretary has said.
Mr Grayling said there would be a "different tone" in British politics if the United Kingdom failed to leave the European Union, and predicted a "less tolerant society" and a "more nationalistic nation".