REUTERS/Francois Lenoi
Tsipras said he was confident that there would be a deal before the country's May 12 debt repayment to the International Monetary Fund, but conceded that "if I end up with a deal beyond the limits, I have no other option, the people will decide."
He added: "The experience we have had so far during the negotiations with the creditors goes beyond likes and dislikes as regarding myself and Varoufakis, it has to do with whether Europe is accepting democracy and the sovereignty of the people."
Those negotiations are over a €7.2 billion (£5.14 billion, $7.84 billion) bailout tranche to tide it over during the summer - but there are still huge chunks of the deal that aren't agreed on. Other European countries want Greece to push through economic reforms which the new government says is against its mandate.
The prospect of a referendum on any deal is pretty uninviting from a financial perspective - any vote would have to be concluded quickly, since the country is running out of money.
Most analysts think that without a deal, Greece will be forced to miss or delay one of the payments in June or July. If Tsipras is wrong, and negotiations stretch on for weeks without a conclusion that the government can sign up up t0, we'll be getting very close to that period.
It's not clear how the Greek people might vote - though anti-austerity parties still seem to hold sway with the public politically, the current negotiation stance of the government is rapidly becoming less popular.
Though they're solidly anti-bailout, the Greek people are still very much pro-euro. Very few seem to want a return to the drachma. If it looked like a failure to reach a deal would see the country ejected from the eurozone, would voters hold their noses and vote for it? It's pretty hard to say right now.
Tsipras skirted away from suggestions that he's sidelined his own finance minister, Yanis Varoufakis, calling him an asset during the interview.