Nigel Huddleston tells Sky News that the clamour for the prime minister to quit is a "complete self-indulgent distraction".
"What's it going to change?" he asks.
The MP for Mid Worcestershire continues: "The EU's negotiating position isn't going to change, the Labour Party's position isn't going to change.
"We had this debate not so long ago and the prime minister won the backing of MPs.
"So I think it's a complete distraction."
On the prospect of giving MPs indicative votes on alternative Brexit options, the Tory vice chairman admits he is "a bit uncomfortable with that".
"I think it would set a dangerous precedent," he says.