Mark Francois has insisted the result of the EU referendum "has to triumph" over the will of pro-Remain MPs.
Appearing on the breakfast show, the European Research Group's deputy chair said MPs were "honour-bound" to respect the Leave result, as rumours of a "coup" to overturn Brexit emerge.
"A group of MPs led by Oliver Letwin and Dominic Grieve - both of whom have lost the support of their local Conservative associations - have basically tried to launch a coup against the British people," he explained.
"It is a coup against the British people."
He added: "The people decided to leave, and MPs are honour-bound to follow that instruction. Woe betide those that don't."
Today, MPs will vote on alternatives to Theresa May's Brexit deal, but Mr Francois insisted Eurosceptics should "hold their nerve".
"On April 10, the European Council have to decide whether to grant us another extension. I passionately believe that they won't," he told talkRADIO's Julia Hartley-Brewer.
"If they don't extend and the coup fails - which I believe it will - the default position is on April 12 we leave the EU. Provided we hold our nerve, in less than two weeks we'll be a free country."