U.S. President Barack Obama has also said that "the United States values a strong UK in a strong European Union."
But German Chancellor Angela Merkel gave Cameron some room for maneuver, indicating she is open to discussions on a "fair compromise."
She is also due to give a speech Thursday at Davos, the annual forum that this year is attended by nearly 40 world leaders and more than 2,000 executives.
Italian Prime Minister Mario Monti, speaking at Davos Wednesday, predicted Britain would remain in the EU.
"I am confident that if there is to be a referendum one day, the UK citizens will decide to stay in the EU and contribute to shape its future," he said. He added, however, "I think the EU does not need unwilling Europeans."
Britain is a net contributor to the European Union and an important player in the single market, which may give Cameron some additional sway. But critics warn he is taking a big gamble.
Former Belgian Prime Minister Guy Verhofstadt, who leads the Alliance of Liberals and Democrats for Europe in the European Parliament, warned against trying "hold the EU to ransom."