Commons Leader Andrea Leadsom said she personally supported the proposal made by Tory Philip Davies (Shipley), telling MPs it would be a “great subject”.
Her remarks came after Mr Davies warned the Commons is out of touch over the European Union, prisoners and overseas aid.
He added such a debate would show if there is “anything at all” in which the Commons is in step with public opinion.
Mrs Leadsom replied: “Well, I think that would be a great subject for a debate. I think it’d probably be a very broad-ranging and well-attended debate.
“I don’t quite know where to start. I’d personally support it. I’ll give it some thought.”
MPs laughed as Mr Davies earlier asked: “Can we have a debate on how out of touch this House is with public opinion?
“The EU referendum proved beyond all doubt that this House is out of touch with public opinion on the EU.
“It’s clearly also out of touch with public opinion on sending more criminals to prison - which clearly the public wants to do, whereas this House always wants to send fewer - and on the splurge in overseas aid, which most people think is ridiculous but people in this House seems to think is wonderful.
“So can we have a debate on this to see if actually there is anything at all where this House is in step with public opinion?”