EU Withdrawal Agreement how MPs could vote.
He also warned that the vote could be a "humiliating defeat" for the ruling Tory Party, especially with numerous backbenchers publicly expressing their opposition and threatening to vote against it in parliament.
Ms Sturgeon has already suggested it would be it would be an "absolute travesty of democracy" if the debate takes place without including someone to make the case for remaining in the European Union.
Mrs May said she was ready to use the G20 summit to correct suggestions by United States president Donald Trump - who is also in Buenos Aires - that her deal would leave the United Kingdom unable to forge a trade agreement with America.
However, fellow Brexiteer Jacob Rees-Mogg has written in the Daily Telegraph of an effort to "frighten and to gull (people) into acquiescing to a non-Brexit Brexit".
On Wednesday, the Bank of England warned that Britain risked suffering an even bigger hit to its economy than during the global financial crisis 10 years ago if it leaves the European Union in the worst-case, no-deal Brexit scenario.
"I ask every member of Parliament to think about delivering on the Brexit vote and doing it in a way that is in the national interest and doing it in a way that is in the interests of their constituents because it protects jobs and livelihoods".More news: Draper launches bid for moon trip
The motion will be backed by the pro-independence Scottish National Party (SNP) and Scottish Greens and the anti-independence Labour and Liberal Democrats.
"A big hit on our economy will mean an increase in local poverty, fewer resources locally to plan and deliver our services, no structured programme to support our local economies and real threats to all aspects of our import and export trade", she said.
With scores of backbench Conservatives threatening to rebel in the historic "meaningful vote", Mrs May might have to rely on Labour votes and abstentions to save her Brexit deal. "In the lead up to what is a crucial vote, you will see more of that". I think we should remember that we gave the vote to the British people as to whether or not to leave the EU.
Mr Corbyn had previously claimed he preferred the bid from broadcaster ITV, but Mrs May wanted the BBC to host it.
Brexiteers have accused the government of betraying the 2016 referendum, as the deal could see the United Kingdom locked in the EU customs union long after the article 50 deadline.
Liam Fox, one of the most senior Brexiters in the British cabinet, has issued a plea to other Eurosceptics to do "what is right for our country" and back Theresa May's withdrawal agreement. "I think it is important we bring the country together and actually look to our future outside the European Union".
She added: "The view I have had from farmers, employers and sector organisations and others in my trips around the country is that they recognise the importance of this deal and they support this deal".
May's comments came after lawmakers proposed an amendment that could stop Brexit if Parliament rejected her agreement.