"We may or may not be able to get an agreement in which case we would have to leave the European Union without one, but we're not going to be bounced into having another referendum", he said.
Asked whether other ministers should quit over the issue, Mr Johnson told BBC Radio 4's Today programme: "I think this is so important that it's up to MPs to take a stand".
The plan emerged after Jo Johnson, a transport minister, resigned from the Government over Brexit and vowed to vote against Mrs May's deal in the House of Commons.
His brother followed in his footsteps yesterday by announcing his resignation as transport minister.More news: WWI: Macron and May pay tribute at Somme
Johnson suggested that other senior Conservatives might be considering their positions, saying that "many are reflecting hard about the deal that's looming and how they will respond to it".
"I mean volley to the left of the them, volley to right of them, and the Prime Minister charges on into the valley of death".
Mr. Johnson the brother of former foreign secretary Boris Johnson whose resignation on July 9th sent the sterling to a 13 month low in August at 1.2662, said that there needs to a public vote on the terms of the UK's departure from the European Union.
As a result, he said it would be a "democratic travesty" if the government did not consult the public on whether they still wanted to leave the world's largest trading bloc.More news: 76ers put end to road struggles with 100-94 win at Indiana
The prime minister is speculated to hold a Cabinet meeting next week to secure the support of her ministers over a Brexit deal she is negotiating with the EU.
The minister said that Britain would not accept separate treatment for Northern Ireland under a Brexit deal, and dismissed calls for a second referendum.
"Well done to Jo Johnson on standing up for what he believes in", she said.
He said: "I think a second referendum would be divisive, but it wouldn't be decisive". "My priority is really just to do my best as a now backbench MP to try and encourage the country to pause and reflect before we do something that is irrevocably stupid", Johnson said.More news: Rays, Mariners Finalizing Trade Centered Around Mike Zunino