MPs have accused the Prime Minister of being "rumbled by her own advisor" over her Brexit plans.
But Mrs May stood her ground during Prime Minister's Questions on Wednesday, ruling out any delay to departure.
She remained adamant the UK will still leave, as currently planned, on March 29.
Video report by ITV News political correspondent Libby Wiener
Henry Smith MP, who represents Crawley, asked the prime minister to explain Robbins' comments.
He said: "Notwithstanding Brussels bar room chatter, will the prime minister rule out a delay of Brexit beyond March 29?"
The question was met with laughs from some MPs.
Responding to the question, the prime minister said: "I'm grateful that he has asked me that question rather than relying on what someone said to someone else as overheard by someone else in a bar.
"It's very clear the government's position is the same.
"We triggered Article 50, in fact this house voted to trigger Article 50, that had a two year timeline that ends of the 29 March. We want to leave with a deal and that's what we are working for."
SNP Westminster leader Ian Blackford called on Mrs May to rule out bringing the meaningful vote to the Commons less than two weeks before March 29.
Mrs May replied: "Of course there is the debate that is taking place tomorrow and then we have made clear that we would bring back, if a meaningful vote hasn't been brought back and passed by this House, we'll make a statement on the 26th February and a debate on an amendable motion on the 27th."
Mr Blackford argued the Prime Minister "continues to run the clock down," as he called on her to extend Article 50.
He said: "This is the height of arrogance from a Government set on running the clock down.
The EU's chief negotiator Michel Barnier refused to comment on Mr Robbins's remarks.
"I don't want to comment on the comment," he told reporters shortly after leaving Strasbourg.
"Just 44 days from a no-deal scenario, the Prime Minister is hamstrung by her own party and rejected by European leaders. The Prime Minister must stop playing fast and loose.
"Businesses are begging for certainty, the economy is already suffering. Prime Minister you've come to the end of the road, rumbled by your own loose lipped senior Brexit adviser.
"Will the Prime Minister now face down the extremists in her own party and extend Article 50?"
Mrs May replied: "He can give business certainty by voting for the deal," adding: "He complains about no deal but of course it was the SNP who wanted to leave the UK without a plan and perhaps we should remind the SNP that independence would have meant leaving the EU with no deal."