LAS VEGAS — Vice President Joseph R. Biden Jr. sat onstage before a crowd of culinary workers here the other morning, listening intently to a man who is not on the ballot but might hold the key to a victory for President Obama in economically ravaged Nevada.

“Mr. Vice President, let me give you some real numbers here,” Senator Harry Reid, the Democratic majority leader, said to union members who had screamed “Harry!” when he poked his head around a curtain. “These people and others have filled 26 field offices around Nevada and have made 3.2 million phone calls. Obama-Biden has 255 team leaders. Mr. Vice President, these folks have registered 70,000 new voters. Three hundred and twenty-five thousand door knocks.”

Mr. Reid has spent the last 10 years building a political machine that helped Mr. Obama win Nevada in 2008 and carried Mr. Reid to a re-election victory two years ago that stunned many pollsters. It is widely praised — even by Republicans — as one of the most effective voter-organizing and money-raising political organizations.

But the Reid machine is facing its biggest test yet.

Mr. Reid’s organization is a large reason that Mr. Obama is favored by many analysts to win narrowly in Nevada, despite what may be the worst economic climate in the nation and a sizable population of voters who, like Mitt Romney, are Mormons. Mr. Reid, who has long been strongly supportive of Mr. Obama in Washington — he maneuvered the president’s health care bill through legislative hoops to an unlikely victory in the Senate — has made it clear that he views a victory for Mr. Obama in his state as a personal mission. This reflects not only his admiration for the president but also his visceral dislike for Mr. Romney, expressed in constant needling and attacks for almost six months.