Tom Tugendhat, who chairs the influential Commons foreign affairs committee, suggested the “meaningful vote” expected to come later this year would be treated as a confidence one.
His comments ramp up the pressure in a row engulfing the Conservatives over parliament’s say in negotiations with the EU.
Some backbench MPs want powers to send Mrs May back to Brussels if they do not agree with her final Brexit deal, or if one has not been reached closer to exit day.
But Brexit Secretary David Davis’ department was defiant.
“We have not, and will not, agree to the House of Commons binding the government’s hands in the negotiations,” a spokesperson said.
Tory rebels, led by former attorney general Dominic Grieve, backed down from threatening to defeat the government over an amendment to its flagship Brexit bill.
They said Mrs May had promised them their concerns would be reflected in a law change tabled in the House of Lords next week.
Speaking to Sky News, Mr Tugendhat said he “thought” MPs would get a “meaningful vote anyway”.
“The meaningful vote is going to be either the government’s deal is accepted, in which case that’s the meaningful vote accepted.
“Or it isn’t accepted in which case, frankly, there’s going to be a new government.”
Mrs May has insisted she will stay on until 2022 and fight the next general election.