At least 23 of the 27 EU member states are expected to form a new Fiscal Stability Union, which would mean stricter budget and debt rules and penalties for those who breach them.
The fiscal union deal was struck at a European summit in Brussels in the early hours of Friday morning - after 10 hours of fraught negotiation - in a bid to stabilise the Euro and solve the debt crisis.
It came after Mr Cameron refused to support an EU treaty change because it would not guarantee London's financial services the protection he demanded.
For years there has been talk of a two-speed Europe. Now it seems to have arrived.
UTV's Business Editor Jamie Delargy
A local economist told UTV he doesn't believe there will be a backlash against Northern Ireland.
"I don't really think that Northern Ireland stands to lose too much on this," University of Ulster economist, Mike Smyth says.
"Our capital in Brussels at the moment is very high. Brussels looks upon Northern Ireland as a success story in terms of the peace process and its own role in Northern Ireland, so this deal will not in any way impact on that."
Another EU watcher, who served for five years as head of the Commission offices in Belfast, is not so optimistic.
"I certainly don't think it will do the UK any good and it means Northern Ireland along with it," Jane Morrice, from the European Economic and Social Committee, said.
"I think that we've been teetering on the edge of European affairs for far too long and I do believe that this is certainly not going to be taken lightly by the other member states."
SDLP South Down MP Margaret Ritchie has also spoken out against Mr Cameron's veto.
She said: "In walking away from the deal on the table at Brussels, David Cameron may be satisfying the Eurosceptic mob in his own party, but he is not necessarily getting the best deal for the UK, much less for the North of Ireland.
"This move by the Prime Minister can only serve to harm our relationship with the EU and create a two-speed, two-tier Europe with those on the inside of the stabilisation deal sorting out the mess, and those on the outside, looking on," the former SDLP leader said.
But Mr Cameron has insisted that Britain will maintain influence in the European Union.
The membership is in our interests and I've always said if that's the case I'll support our membership. Membership of the European Union is good for us.
David Cameron
"Europe has many rooms. I think Britain should feel the Europe we want has got the flexibility of a network," Mr Cameron said.
"You've got to form alliances in Europe for the things you want to get done. I don't think anything that happened last night will change that, in fact it was relatively, there was obviously fundamental disagreement - a situation where Britain had to say it couldn't go ahead with this treaty - but it was done in a very good natured way."
Meanwhile, the Irish Government is getting legal advice on whether a referendum needs to be held on the new European deal.
Taoiseach Enda Kenny said its Attorney General Marie Whelan will have to forensically examine the deal struck in Brussels.
"The first thing is that once the text has been approved and agreed every country has to do its own thing," said Mr Kenny.
"In our case the Attorney General will have to analyse that, forensically examine it and give official and formal information and advice to the Government as to whether a referendum is required or not."
"Obviously I wouldn't speculate on that because I'm not confident to do so," he added.
Mr Kenny was positive about the outcome of the meeting in Brussels.
"Ireland's economic security has been defended and protected," he said.
"A great deal of useful work was done in respect of putting firewalls to prevent contagion and the substance of this has now been agreed and requires to be checked and analysed by each individual country.
"Specifically in Ireland's case, I raised the exceptional difficulty that Ireland's gone through in having to borrow very extensively prior to the bailout for bank recapitalisation and the challenges that faces for us and I placed that firmly on the table."