By Adam Nagourney, New York Times

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,” Sen. 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.”

Reid has spent the last 10 years building a political machine that helped Obama win Nevada in 2008 and carried 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.

Reid’s organization is a large reason that 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. Reid, who has long been strongly supportive of 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 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.

Even more ambitiously (and perhaps more problematically), Reid is determined, friends say, to lift Representative Shelley Berkley, a Democrat, to victory over Sen. Dean Heller, a Republican, as he seeks to make sure that he does not return to Washington next year as the Senate minority leader.

Romney is campaigning here for two days this week — both he and Obama were in the state on Wednesday — backed up by a surge of new advertising, reflecting the importance that both he and the president have placed on this state’s six electoral votes.

In a contrast that has been noted by the Romney camp, the Nevada Republican Party has collapsed in a storm of factionalism and infighting between Tea Party conservatives and party regulars. A contingent of supporters of Representative Ron Paul of Texas, an unsuccessful Republican presidential candidate, ousted the party leadership in a showdown in the spring.

Romney’s campaign responded by building a parallel political organization, Team Nevada, to match the combined forces of the Reid organization and Obama for America, which built on what Reid had in place. Aides to Romney said they had made considerable progress. Hundreds of Romney volunteers, many bused in from Southern California and Utah, gathered recently outside the campaign’s headquarters at a Las Vegas shopping center before heading out in white vans to knock on doors in Clark County.

Still, the aides did not dispute the advantage that Reid had created for the president.

“Turnout is going to be important,” said Ryan Erwin, Romney’s senior adviser here. “And, candidly, the Reid machine and the Democrats have been better and more disciplined than we have been for the better part of a decade.”

For all the ways that presidential elections are portrayed as national affairs — and for all the technology that has transformed the relationship between candidates and voters — the basic get-out-the-vote mechanics that have empowered political organizations for 100 years remain critical in elections. (Or, at least, close elections. A good organization can, at best, add two or three percentage points to a candidate’s vote share, analysts said.)

The Reid army may be using modern tools — volunteers can be spotted walking through neighborhoods with iPads linked to headquarters, feeding and updating information on potential voters — but the intent is the same as ever: finding people who like your candidate and making sure they vote.

“Reid, working with various leaders of the Democratic Party, put together a very effective voting machine that’s gotten better every election,” said Eric Herzik, a professor of political science at URN. “Reid is the conduit to money for candidates, he is a conduit to organized labor, and he has great relations with multiple groups around the state.”

Several early indicators have attested to the effectiveness of the Democratic machine, which draws on the state party, powerful unions like the culinary group Reid spoke to last week, and the staff members and resources the Obama campaign dispatched to this state.

Voter registration in Nevada closed earlier this month, leaving the Democrats with an edge of 90,000 voters over the Republicans, up from an advantage of 60,000 voters two years ago, the secretary of state’s office reported. (Reid understated the figure in his speech last week.) Democrats have substantially outpaced Republicans in early voting, another way to measure political organization.

The obstacles for Obama here are considerable. The state’s unemployment rate was 11.8 percent in September, a drop from 12.1 percent the month before but still the highest in the nation, and the state has been racked by mortgage foreclosures.

“I don’t think that anyone believes that Obama supporters are going to be as motivated this year as they were in 2008,” said Mason Harrison, the communications director for Romney’s campaign here.

In Reid, Republicans face an opponent who is fiercely combative and wily, with a command of the ebbs and flows of his state. He is loyal to those he likes (Barack Obama) and unrelenting against those he does not (Mitt Romney).

He has been one of Romney’s top tormentors, at one point claiming that he had failed to pay any federal income taxes for the past 10 years, an assertion that was debunked when Romney released information on two years of income taxes.

“The man who is leading the Republican ticket for president of the United States is giving used-car salesmen a bad name,” Reid said at the rally here.

Reid’s campaign to rebuild the Democratic Party was motivated by self-preservation after he almost lost re-election to John Ensign in 1998 and Republicans went on in 2002 to sweep every contested statewide office.

He displayed his ability to turn out voters in 2010 when he defeated his Republican opponent, Sharron Angle, by five percentage points, after many analysts — and polls — predicted that he was headed for defeat.

Herzik said he had followed Reid workers to observe their efforts in neighborhoods. “They are like dogs on meat,” he said.

Erwin, the Romney adviser, said that for all the work he and other Republicans had done to catch up, he did not dispute that characterization.

“We do know how to run Republican organizations here — for the first time since 2002, the Republican Party is strong,” he said. “But I don’t harbor any misconceptions that we’ve caught up to something that Democrats have built up over a decade.”