But scores of Conservative lawmakers signaled that they would press ahead with plans to force a parliamentary vote on Wednesday which they are almost certain to lose but which is likely to embarrass Mr. Cameron by highlighting his party’s turmoil over Britain’s ties to the 27-nation European bloc and a profound split over the same issue within his coalition government. During a visit to Washington by Mr. Cameron on Monday, Mr. Obama urged Britons not to give up on their membership in the union without first seeking to improve it. “You probably want to see if you can fix what is broken in a very important relationship before you break it off — that makes sense to me,” Mr. Obama said, while stressing that any decision was for the British people. The statement reflected growing worries that one of America’s closest allies is moving toward leaving the bloc. Mr. Cameron has pledged an “in-out” referendum on British membership in the European Union by 2017 if he wins the next election in 2015. But he did not include that promise in a traditional legislative program delivered last week by Queen Elizabeth II. According to British news reports, almost 80 rebellious Conservatives are promoting a parliamentary vote on Wednesday to castigate Mr. Cameron for the omission, demanding that the referendum pledge be enshrined in law immediately. Mr. Cameron’s spokesman said the prime minister would counter by publishing his own draft legislation later on Tuesday “to show the strength of his commitment to hold an in-out referendum.” But it was not clear whether the maneuver would satisfy the vocal euroskeptic wing of his party. The draft legislation does not have the support of the junior coalition partners, the Liberal Democrats. Mr. Cameron’s spokesman said that the decision to produce the draft bill as a Conservative Party initiative reflected the fact that the prime minister’s view on Europe “is clearly different” from that of Deputy Prime Minister Nick Clegg, who is the leader of the Liberal Democrats. “The prime minister felt, as he has made clear in the past, that he was always keen to look at all options to show the strength of his commitment to hold an in-out referendum, and he felt that this was the best course of action,” said Mr. Cameron’s spokesman, who is not normally identified by name in line with government policy. The timing of the debate in the Conservative Party was particularly awkward for Mr. Cameron, who used his visit to Washington to push for a free trade area for the European Union and the United States, a long-cherished objective of policy makers, and one that the British prime minister said would benefit the global economy. Britain holds the G-8 presidency, and Mr. Cameron will lead the annual gathering of the group next month in Northern Ireland. His meeting with Mr. Obama was part of his preparations for that meeting. At the news conference in Washington, Mr. Cameron repeated his strategy of renegotiating Britain’s ties with the union before holding a vote on membership in 2017. He insisted that there was “not going to be a referendum tomorrow,” saying that to hold one now would present a “false choice between the status quo and leaving, and I don’t think that’s the choice the British public wants or the British public deserves.” Earlier, Mr. Cameron said other critics within his party who dismissed his prospects of negotiating a new deal with the union were taking an “extraordinary” position and “throwing in the towel before the negotiations even started.” Such strains in British politics are nothing new, and deep divisions over Europe have afflicted the Conservative Party on and off for a quarter of a century, contributing to the downfall of the party’s two last prime ministers. In 2006, soon after he took over the leadership of his party, Mr. Cameron warned colleagues that they had alienated voters by “banging on” about Europe and tax cuts. When the issue refused to go away, Mr. Cameron had hoped that, by going further than any of his predecessors in offering Britain’s first referendum on Europe since 1975, he would persuade his party to unite behind his strategy. Though surveys show Britons to be highly skeptical about the European Union, it tends to be an issue well down their list of priorities. But the rise of the populist U.K. Independence Party, which wants Britain to quit the union, has sent shock waves through the ranks of Conservative lawmakers. The idea of quitting the bloc, which was once seen as the preserve of a tiny, extreme faction of the party, is gaining respectability after endorsement by two former cabinet ministers last week. Meanwhile, ministers seeking support on the right of the party have been stressing their euroskeptic credentials. Knowing the strength of feeling within his party, Mr. Cameron has allowed ministers to abstain and his party’s other lawmakers to vote against on Wednesday if they choose, a rare and unusual concession. But Emma Reynolds, a spokeswoman on Europe for the opposition Labour Party, told the BBC that the Conservatives were demonstrating their well-known divisions over Europe. “It is history repeating itself,” she said. “We have seen this for the last 20 years — they are in complete chaos and disarray.”