An Oct. 18 article misstated the margin of President Bush's 2000 victory over Al Gore in Arizona. Bush won the state 51 percent to 45 percent. (Published 10/19/04)

Amid the frescoed ceilings and pseudo-Renaissance splendor of the glittering Venetian casino, Bruce Goldenson watched a merciless slot machine swallow another $5. He turned away in disgust.

"I've got to do something useful while I'm here," the tourist from Arizona muttered. "I read that Bush is in Vegas this morning, and I almost went over to hear him. But I think he's way across town."

Of course, if Goldenson wanted to see a presidential candidate in this city, he didn't have to travel that far. The same morning last week when President Bush was speaking at the University of Nevada at Las Vegas, John F. Kerry was campaigning barely a block from the casino where Goldenson was losing his money. First lady Laura Bush was stumping on the Vegas strip the same day. And Teresa Heinz Kerry was also in Nevada, at a Democratic rally in Reno.

By traditional rules, it would seem crazy for the campaigns to put that much firepower into a state with just five electoral votes less than three weeks before Election Day. But the 2004 election is so close, and the remaining battleground states so few, that Nevada and its southwest neighbors have become prime targets for both campaigns.

Of the five states in the "Cactus Corridor" of the desert Southwest, only one -- Utah, a Republican stronghold -- seems firmly decided. Arizona, where polls showed a dead heat at the end of the summer, moved strongly to Bush in September, but the Democrats now say they are clawing back. Nevada, New Mexico and Colorado all appear to be up for grabs.

As a result, the major candidates have been constant visitors this fall to a region that barely saw any presidential campaigning four years ago. In the past two weeks, the presidential contenders and their running mates have been to Denver and Colorado Springs, Albuquerque and Santa Fe, Reno and Las Vegas, Phoenix and Tempe.

But they have also found time to campaign in the oil-patch hamlet of Hobbs, N.M., in the desert town of Henderson, Nev., and in the shopping-mall suburb of Commerce City, Colo.

In demographic terms, it makes sense for the candidates to move toward the Southwest, because millions of voters have moved in this direction in recent years. The four southwest battleground states gained five electoral votes since the 2000 election. If either candidate could sweep Arizona, Colorado, Nevada and New Mexico, the total of 29 electoral votes would be a bigger prize than Florida.

Much of the in-migration has been low-income workers, particularly Hispanic, coming for jobs in the tourism industry -- hotel maids, ski lift attendants -- that tend to pay close to the minimum wage. Organizations such as Moving America Forward, a creation of New Mexico Gov. Bill Richardson (D), have been energetically registering these newcomers to vote.

The result has been particularly dramatic in Nevada. Republicans here had a 14,000-vote advantage in registered voters in January. When registration closed on Oct. 12, preliminary registration figures showed that Democrats had pulled even or perhaps slightly ahead. Normally, new registrants turn out in large numbers for their first election.

There has also been a push to sign up new voters on Indian reservations, where the vote tends to be strongly Democratic. Indian turnout is expected to increase significantly in New Mexico and Arizona because the Navajo Nation, with 300,000 voters, has scheduled its tribal election this year for Nov. 2, the same day as the presidential vote.

Still, the Democrats are playing catch-up in a region that had been largely Republican. In the 2000 election, Bush carried Arizona, Nevada and Colorado comfortably with minimal personal campaigning; he lost New Mexico by a smidgen.

Republican leaders say the established voting pattern will reemerge on Election Day.

"Yes, we've got a close race this year," says Colorado Gov. Bill Owens, a strong Bush ally. "But I expect we're going to see the Republicans come home when it's time to vote. The polls show that is already happening in Arizona. I think we'll see the same thing in Colorado. And the president is personally popular in New Mexico, which probably explains why we're running even there."

Bush won Colorado by 51 percent to 43 percent in 2000. This time, some polls give the president a small lead, but several have shown the race as nearly even. The large active-duty and retired military population in the state is expected to give Bush a boost. Still, there is some anger among military families living near the Army's Fort Carson, where nearly every one of the 15,000 soldiers has been to Iraq and ordered to return for another tour.

Kerry is benefiting in Colorado from the coattails of two members of a prominent Democratic family. State Attorney General Ken Salazar seems to be leading in a close race for Colorado's open Senate seat; his brother, John Salazar, seems likely to win the race for the open House seat that covers the western half of the state. The two Salazars are expected to inspire a record turnout among Hispanic voters in the state, a bloc that tends to vote Democratic in presidential races as well.

Also in Nevada, where Bush won by 50 percent to 46 percent in 2000, the Senate race is a plus for the Democratic ticket. The state's most powerful politician, Sen. Harry M. Reid (D), looks like a shoo-in for a fourth Senate term. Reid has been campaigning vigorously for his friend Kerry, savaging Bush every day on an issue that resonates across party lines here: the Bush administration's decision to put the national nuclear waste dump site at Yucca Mountain, Nev.

In 2000, Bush told Nevadans he would base his decision about a nuclear waste site on "sound science." Republicans say he did that, but the Democratic position is that the state has been betrayed. "George Bush broke his promise to Nevada," Reid declares in a hard-hitting TV ad that is running constantly in the state's two major media markets. Kerry cast some Senate votes that could be construed as favoring a dump site at Yucca Mountain, but he has come out forcefully against it this year and has made the point on each of his five campaign trips to the state.

Bush won Arizona by 54 percent to 51 percent in 2000, and last month statewide polls showed him with a double-digit lead. The Kerry camp cut its advertising budget in the state, and political pros considered the state all but decided.

But the president has lost some of the advantage in October, recent polls show. When Kerry went to Arizona for the campaign's third debate last week, Gov. Janet Napolitano (D) pleaded with him to allocate more time and money to a state she said was winnable, according to Kerry staffers.

"I would think that Bush is still ahead here, but not by double digits any more," says Bruce Merrill, a pollster and political scientist at Arizona State University. "It's still a Republican state. It's still pretty much Barry Goldwater country. But we have a bloc of independent voters in Arizona who can turn any election. Bush seemed to have them in his hand in September. In the debates, though, I don't think there's any doubt that Kerry won. That didn't change the partisans, but I think we're going to see some of that independent vote here shifting to Kerry."

Al Gore carried New Mexico in 2000 by less than a half a percentage point. But Richardson won the gubernatorial race easily in 2002, and Democrats have been counting the state as a "likely" for Kerry since last winter.

Bush moved into a small lead, however, in September polls there, at a time when the "flip-flop" attack was undermining Kerry's appeal. Kerry came back after the first debate and showed a three-point lead statewide in an Albuquerque Journal poll at the beginning of October.