Mr Tusk will chair a crucial summit meeting in Brussels on Thursday on the controversial proposals.
Poland and three other countries are reported to be still resisting welfare curbs while France is thought to be against financial regulation changes.
A new draft deal is due to be published later, ahead of the two-day summit.
Asked by the BBC’s Ben Wright whether he would get a deal, Mr Tusk said: “I am sure that we have no choice.”
In a letter to the leaders of the 28 member states, Mr Tusk said the summit “will be a crucial moment for the unity of our Union and for the future of the United Kingdom’s relations within Europe”.
“After my consultations in the last hours I have to state frankly: there is still no guarantee that we will reach an agreement.
“We differ on some political issues and I am fully aware that it will be difficult to overcome them. Therefore I urge you to remain constructive.”
He said the negotiations were at a “very advanced” stage and failure now “would be a defeat both for the UK and the European Union, but a geopolitical victory for those who seek to divide us”.
Mr Cameron is working on a separate plan to boost UK sovereignty aimed at getting sceptical Tories, including Boris Johnson, to get behind his reform deal.
Mr Johnson – who is being touted as a possible leader of the out campaign – has met Mr Cameron at Downing Street.
“I’ll be back,” he told reporters as he left Number 10, adding: “No deal, as far as I know.”
BBC assistant political editor Norman Smith said the London mayor, who is “pivotal” to Mr Cameron’s plans, would keep the PM waiting until he had returned from the summit before announcing which camp he would support, although his “no deal” comment was not thought to be a reference to his own concerns about sovereignty.
Sources close to Mr Johnson say his decision on whether to back remaining in or leaving the EU is “very finely balanced”.
They say the decision by Mr Cameron to try to sell his proposed deal to Mr Johnson underlines how crucial he is likely to be if the prime minister is to win the referendum.
“They are pretty determined to get him on board,” the source added.
They have strongly rejected suggestions that Mr Johnson’s decision is tied to his ambitions to lead the Conservative Party when Mr Cameron steps down.
“His decision is in no way predicated on any leadership question. It’s based on what he thinks will be in the best interests of the country,” the source said.
Mr Cameron’s sovereignty plan is expected to suggest extra powers for the UK Supreme Court to protect UK law from challenges from the European Court of Justice, to assert the primacy of UK law over Brussels.