The minister, who is the only member of David Cameron’s 2015 Cabinet still in his original post, warned that the increasingly polarised positions of the factions are not “generally acceptable to the wider public”.
Mr Mundell, who made the intervention ahead of Brexit Secretary Dominic Raab’s resumption of negotiations in Brussels, told news website Politico that there is no alternative to Theresa May’s plan.
Speaking to Politico’s morning newsletter, Playbook, he said: “People have to wake up to what the alternatives are.
“I think people have to be challenged. If they don’t like the Chequers deal, what is their alternative?”
He added: “Clearly there is a group of people who would just leave the EU at any cost, in any circumstances.
“And there is another group of people who would go back into the EU. Neither of those alternatives, I think, are generally acceptable to the wider public, nor would be of benefit now to the country.
“I think there is a growing reality that, other than extreme positions, there isn’t an alternative.”