WASHINGTON — In a Paris hotel room on Monday night, Secretary of State Hillary Rodham Clinton found herself juggling the inconsistencies of American foreign policy in a turbulent Middle East. She criticized the foreign minister of the United Arab Emirates for sending troops to quash protests in Bahrain even as she pressed him to send planes to intervene in Libya.

Only the day before, Mrs. Clinton — along with her boss, President Obama — was a skeptic on whether the United States should take military action in Libya. But that night, with Col. Muammar el-Qaddafi’s forces turning back the rebellion that threatened his rule, Mrs. Clinton changed course, forming an unlikely alliance with a handful of top administration aides who had been arguing for intervention.

Within hours, Mrs. Clinton and the aides had convinced Mr. Obama that the United States had to act, and the president ordered up military plans, which Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, hand-delivered to the White House the next day. On Thursday, during an hour-and-a -half meeting, Mr. Obama signed off on allowing American pilots to join Europeans and Arabs in military strikes against the Libyan government.

The president had a caveat, though. The American involvement in military action in Libya should be limited — no ground troops — and finite. “Days, not weeks,” a senior White House official recalled him saying.