On Friday evening, the US, China, India, Brazil and South Africa reached a last-minute agreement on a number of issues, such as a recognition to limit temperature rises to less than 2C (3.6F).
However, BBC environment correspondent Richard Black says the language in the text shows 2C is not a formal target, just that the group "recognises the scientific view that" the temperature increase should be held below this figure.
'Devoid of morality'
Mr Obama said the deal would be a foundation for global action but admitted there was "much further to go".
However, a number of developing nations were angered by the draft proposals.
Lumumba Stanislaus Di-Aping, the Sudanese negotiator, said the draft text asked "Africa to sign a suicide pact".
AT THE SCENE
Richard Black, BBC News environment correspondent
While President Obama was on TV announcing he'd secured a new global climate deal, most other delegations here had not even seen it.
Initially he had the support of just four other countries - Brazil, China, India and South Africa. The EU came on board - albeit reluctantly - and so have most developing countries
But the way the deal was done and announced, and its weak provisions, seriously annoyed a number of countries - a "coup d'Etat against the UN".
With no firm target for limiting the global temperature rise, no commitment to a legal treaty and no target year for peaking emissions, countries vulnerable to climate impacts are pointing out this "deal" does not guarantee the temperature targets they need.
Saying it was "devoid of any sense of responsibility and morality", he added: "The promise of $100bn will not bribe us to destroy the continent."
The five-nation deal promised to deliver $30bn (£18.5bn) of aid for developing nations over the next three years, and outlined a goal of providing $100bn a year by 2020 to help poor countries cope with the impacts of climate change.
The agreement also included a method for verifying industrialised nations' reduction of emissions. The US had insisted that China dropped its resistance to this measure.
During the two-week gathering, small island nations and vulnerable coastal countries have been calling for a binding agreement that would limit emissions to a level that would prevent temperatures rising more than 1.5C (2.7F) above pre-industrial levels.
"Can I suggest that in biblical terms, it looks like we're being offered 30 pieces of silver to sell our future," Tuvalu's lead negotiator Ian Fry said during the main meeting. "Our future is not for sale."
"Of course it is not what we were looking for, and I will be the first person to be unsatisfied; but this document allows us to continue negotiations and to have a procedure leading to a binding legal agreement within 2010. I urge all countries to back this, and do not let these talks collapse."
British PM Gordon Brown said the deal had almost universal backing: "Let's remember, a year ago nobody thought this sort of agreement was possible."
Delegates are still angrily debating the deal and there are doubts whether Danish PM Lars Loekke Rasmussen will be able to declare it approved.
But the majority of speakers addressing the conference have been urging the Danish hosts to adopt the proposed text, saying the US-led deal was better than no deal.
EU Commission President Jose Manuel Barroso told reporters: "I will not hide my disappointment regarding the non-binding nature of the agreement here."
It is now evident that beating global warming will require a radically different model of politics than the one in Copenhagen
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