Britain still faces "a lot of hard work" to secure an acceptable deal on EU reform and to persuade the other 27 member states to sign up to changes, Downing Street has said.
Intensive negotiations were under way between diplomats in Brussels on Monday to finalise a package to be put to the EU's 28 national leaders in time for an early in/out referendum.
European Council president Donald Tusk approved a 24-hour extension after a Sunday evening meeting with the Prime Minister, which delivered what Number 10 termed a "significant breakthrough" over migrant benefits, but failed to reach agreement on a number of other areas.
Mr Tusk hopes to present EU leaders as early as Tuesday with a draft text of his proposed solutions to the UK's concerns over migration, sovereignty, competitiveness and protection for non-eurozone countries, for discussion at the upcoming Council summit on February 18-19.
Agreement in February is regarded as crucial if the referendum is to be staged before the summer holidays.
Downing Street said the PM had secured a significant assurance that a proposed "emergency brake" on welfare payments to EU workers could be triggered immediately after a vote to remain in the EU, on the basis of existing levels of immigration.
Mr Cameron's official spokeswoman insisted that Britain had made "substantial progress", but added: "There is more work to do in all four areas - more work in some areas than in others."
She told a regular Westminster media briefing: "There is more hard work to be done both in terms of the proposals that are tabled and how far they go in addressing the reforms we are seeking, but then - let's be clear - in the run-up to either the February European Council or whenever we get a deal, there will be a lot of hard work to get 27 other member states signed up to what we need.
"There is a lot still to do."
It remained unclear how the proposed emergency brake would operate and who would have the final say on when the measure could be activated and how long it would remain in effect.
The mechanism has been put forward by Brussels as an alternative to Mr Cameron's plan to impose a unilateral four-year curb which other member states ruled out as discriminatory and in breach of the freedom of movement principle.
The PM agreed to accept it as a "stop-gap" measure - on the condition he received assurances the existing pressure on the UK would meet the threshold to trigger it and it could remain in place.
One critical stumbling block is the UK's demand for it to be allowed to remain in place "long enough to resolve the underlying problem" - perhaps as long as seven years.
Supporters of British withdrawal from the EU dismissed the frantic round of negotiations - which saw the PM cancel a planned trip to Scandinavia last week for hastily-arranged talks with European Commission president Jean-Claude Juncker - as a choreographed display designed to convince voters that Mr Cameron has been forced to fight hard for significant concessions.
Ukip deputy leader Paul Nuttall said: "The theatrics and drama of David Cameron's sham renegotiation continues and he is playing us for fools.
"In 24 hours when - to no doubt great fanfare - Cameron returns with a 'deal' with Brussels, it looks like it'll be nothing more than tinkering round the edges of our relationship with the European Union and will not go any way to dealing with the wholesale loss of sovereignty to the EU, the eye-watering cost of it, or indeed go any way to bring back genuine control of our borders from the EU."
Matthew Elliott, chief executive of the pro-Brexit Vote Leave campaign, said: "The final outcome of these negotiations will be a set of deeply trivial reforms that won't bring powers back from Brussels.
"Even with the avalanche of spin that will accompany the final deal, the renegotiation won't take back control for the British public. The only way to do that is to Vote Leave."
But Mr Cameron's spokeswoman denied the wrangling was confected: "I wouldn't accept that at all. Look at the amount of hard work, time and effort the Prime Minister, other senior ministers and senior Government officials have had to put into this. Look at the work we have had to do with a number of other European countries who have raised concerns.
"These are significant, far-reaching reforms and that is why it is taking time."
She insisted Mr Cameron was still willing to wait until the end of next year to hold the referendum, in order to secure the best possible reforms for Britain: "The PM is most focused on getting the right deal. That is what matters. We are not in a hurry."
Among the proposals currently on the table were reforms to prevent non-EU nationals using sham marriages with Europeans in order to maintain their right to remain in the UK, she confirmed.
But she denied suggestions that the UK was seeking a veto over further integration in the eurozone, insisting that Britain was instead asking for a mechanism to be created to ensure any concerns from non-single currency members are properly addressed.
"We have been clear throughout that it isn't about the UK being able to veto further eurozone integration," she said.