The Prime Minister was forced to make the embarrassing decision after discovering his chosen date clashed with a key Franco-German anniversary.
Instead of taking place next week, the speech has been hurriedly rushed forward to this Friday.
Mr Cameron had initially planned to make his call on January 22, only to find out that date was the 50th anniversary of the Elysee treaty between France and Germany, which signalled a new period of reconciliation between the two countries.
Earlier, Mr Cameron for the first time raised the prospect the UK could leave the EU, in a move that will significantly increase pressure on his Government to act over Europe.
His comments come just days after Chancellor Gorge Osborne warned the EU had to change or risk losing the UK.
The PM insisted it would not be in the UK's interests to leave. But in a notable change in language ahead of a keynote speech on the issue next week he said the UK would not "collapse" if there were to be a so-called "Brexit". The Conservative leader has also launched a charm offensive to convince other EU leaders of his case that the UK's relationship needs to be renegotiated.
Over the weekend the PM spoke to Angela Merkel, the German chancellor, and Mark Rutte, the Dutch prime minister, as well as the French President Francois Hollande.
Mr Cameron's official spokesman described the discussions as "very friendly and constructive" but refused to be drawn on whether the PM had been pressurised to change the speech date.
Earlier, Mr Cameron had said the UK would not "collapse" if it left the EU. He reiterated his commitment to membership and told eurosceptic members of his party they would have to wait until after 2015 for a referendum on the issue.
He also denied claims by the German Government last week that the UK was attempting to blackmail the rest of Europe.
Mr Cameron said: "I'm not blackmailing anybody. Britain, just like every other European country, has a perfect right to say 'we are members of this club, we are prominent members, we pay a large bill for being a member of this club; we're perfectly entitled to argue it needs to change'."