WASHINGTON, June 3 — On a Tuesday afternoon two months ago, Secretary of State Condoleezza Rice sat down to a small lunch in President Bush's private dining room behind the Oval Office and delivered grim news to her boss: Their coalition against Iran was at risk of falling apart. That question touched off a closely held two-month effort to reach a drastically different strategy, one articulated in a single sentence that Ms. Rice wrote in a private memo to the president. It broached the idea that the United States end its nearly three-decade-long policy against negotiating directly with Iran.