LAS VEGAS - In a state where so many fortunes have changed on a roll of the dice, the odds seemed to favor Mitt Romney on Saturday. Mr. Romney, a former governor of Massachusetts, led on Saturday in the early results from the Nevada caucuses, the first nominating contest in the West. He had 37.7 percent of the caucus vote. Following Mr. Romney was Representative Ron Paul of Texas with 29.7 percent; Newt Gingrich, a former House Speaker, with 19.8 percent of the vote; and Rick Santorum, a former senator from Pennsylvania, with 12.9 percent. Results from Nevada's largest county, Clark, which includes Las Vegas, will not be released until later tonight. If the results stand through the night, they would further deflate the once-vital challenge posed by Mr. Gingrich, who is seeking to make his way through an expected rough few weeks of political weather before what he hopes will be strong enough showings in the 10 states that vote on March 6 - "Super Tuesday" - to revive his chances. Far from competing with Mr. Romney here on Saturday, early results showed that Mr. Gingrich in a race with Representative Ron Paul for second place.Nevada is considered almost home turf for Mr. Romney, who is Mormon. The state has a large Mormon population, who made up roughly a quarter of Republican caucusgoers, according to entrance polls. And it shares a border with Utah, where Mr. Romney won credit for saving the troubled 2002 winter Olympics. The state has been particularly hard hit by the housing downturn, and the top issue on the minds of caucusgoers on Saturday was the economy, according to entrance polls on Saturday. In addition, more than 4 in 10 of the caucus goers surveyed Saturday said the quality that mattered most to them in a candidate was his ability to beat President Obama in the fall. The poll was conducted by Edison Research for the National Election Pool of television networks and The Associated Press. Already looking ahead to the next contest, Mr. Romney campaigned Saturday afternoon in Colorado, which holds its caucus on Tuesday. In a speech in Colorado Springs, Mr. Romney kept his focus on President Obama, never mentioning any of his Republican rivals by name. Referring to the recent unemployment numbers, which were announced Friday to be at a three-year low, Mr. Romney tried to turn the tables on the president. "He's celebrating that it's at 8.3," Mr. Romney said. That's still above the emergency line of 8 percent. Mr. Paul began building his organization in Nevada early. But he made it clear on Saturday that he is more focused on drawing attention to his issues of limited government, limited deficits and a restrained military than on winning. Before the final results were released in Nevada, Mr. Paul on Saturday addressed a boisterous crowd of supporters with a trademark speech in Minnesota, which holds its primary Tuesday. "Something pretty big is happening in this country," he told the crowd, portraying the support he did have in Nevada as a vote for, "less government, less war, and a free-market economy." Mr. Paul described his normal list of problems that need fixing in Washington, including the monetary system, the Federal Reserve, the making of war and government intervention in private business. Earlier in the day, at Valley High School in Las Vegas, Mr. Romney appeared to have a lot of support among the more than 200 caucusgoers who packed the school parking lot. The "electability" argument - that Mr. Romney is the candidate most capable of defeating President Obama - seemed to explain much of his backing, interviews here suggested. Trip Gabriel contributed reporting from Las Vegas, Ashley Parker from Colorado Springs, and Michael D. Shear from Minnesota.