Mr Duncan Smith said the UK had "faced bigger trials than this".
"It has stood alone in war but it has also defined trade around the world...Britain is a phenomenal country. It has stood alone and fought for freedom. It has been a global trader, it can again be a global trader.
"Why would we have such a low opinion of the British people that we going about talking about a leap in the dark and profound shocks?"
Asked whether he believed the PM's argument lacked patriotism, he replied: "It is not about personalities but the In Campaign's whole strategy has been about saying 'basically we are too small, too little, inconsequential, we can't do what we want. I don't know why anyone would want to run a country like this."
While the EU was an important trading partner, he said the level of two-way trade had been exaggerated. If the UK voted to leave the EU, he said, it would be able to negotiate a simpler trade-based relationship enabling it to have "access to the world and to the EU".
"We do a deal with the EU. That is a trade deal, it is about access to our markets and access to theirs. Part of our red lines would be about us being able to control our borders as we want…That deal is very doable."
The former Conservative leader also rejected suggestions that an Out vote could trigger the break up of the UK, saying the idea that it could provoke another independence referendum in Scotland was "absurd".
Mr Duncan Smith's intervention was welcomed by the Vote Leave campaign group, which tweeted: "All the government has is project fear - we will be explaining to people project hope, how Britain and EU will be better after we take control."
But pro-EU campaign group, Britain Stronger in Europe, said Mr Duncan Smith had failed to explain how the UK could retain access to the European single market while not upholding principles of freedom of movement.
And small business minister Anna Soubry, who is campaigning to stay in the EU, said leaving would be "chaotic" and stall a much-needed process of economic reform.
"If people vote to stay in, we will remain within a reformed EU with a wind of change I believe is blowing right across it," she told Radio 5 live's Pienaar's Politics.
"Colleagues from other countries are really talking about the need to advance the programme of deregulation, fewer directives, that we have led."
Labour's Angela Eagle accused eurosceptics of wanting to turn the clock back to the 1970s and focusing trade strategy on the rest of the Commonwealth.
"Their attention is elsewhere so we have to have to make the best of where we are," she told Marr.
"I believe that we should be confident about our values and we can project our values if we work through international organisations and the EU is one such organisation."
She claimed it "would be Labour votes" which keeps the UK in the EU and the party was "absolutely united in our determination that we get the right decision".