WASHINGTON – The sizzling presidential race shifts to a desert stage in Arizona this week for a last showdown on the heavyweight debate circuit.

President Bush’s forceful performance Friday night in St. Louis won generally stronger reviews than his first face-off with Sen. John Kerry. But Kerry also turned in a strong performance, and the battleground now moves to subjects that may prove friendlier for him. The topics in the debate in Tempe, Ariz., will be restricted to domestic issues like jobs and health care, and polls show stronger support for Kerry’s stances on these topics than for his positions on foreign policy.

The final debate will be televised from Arizona State University at 9 p.m. EDT Wednesday.

On Friday night at Washington University in St. Louis, the candidates appeared to travel different paths: Bush did his best to firm up his Republican base and avoid the stylistic gaffes that tarnished his first debate performance.

Meanwhile, Kerry tried to reach out to undecided voters and sway those not sold on his capacity to lead.

In a Gallup survey taken for CNN and USA Today just after the town hall meeting, 47 percent said that Kerry had won and 45 gave the edge to Bush – a virtual draw.

An ABC survey found that 44 percent considered Kerry the winner, with 41 percent saying Bush had done the best, also a statistical tie.

Several debate experts praised Bush’s revival in the town hall setting following the president’s lackluster performance when he faced Kerry eight days earlier in Miami.

“I think that the story of this debate is that Bush came back after the first debate. He was more animated, and he worked the crowd well,” said David Lanoue, chairman of political science at the University of Alabama and a debate expert. “I think John Kerry did well enough. But because expectations changed after the first debate, it’s probably going to benefit Bush,” added Lanoue, author of “The Joint Press Conference: The History, Impact, and Prospects of American Presidential Debates.”

Heading into the final debate, Bush’s principal opponent may well be unfolding news as much as Kerry. As his campaign worked in recent days to plant doubts about Kerry’s qualifications, that message has been clouded by the negative reports both on Iraq and the economy.

Voters making up their minds are seeing and reading about violence in Iraq that shows no signs of abating.

The president also has faced the challenge of convincing voters that the economy has turned the corner in light of government reports. Bush would have far preferred to take the stage at Washington University trumpeting the creation of new jobs under his watch.

Instead, he had to endure criticism from Kerry hours after the release of the fourth consecutive monthly report of disappointing job creation.

Bush also might be entering the final debate in Arizona at a disadvantage because the topics are limited to domestic issues. Voters often give Kerry higher marks on ability to handle the economy, health care and other domestic issues, while Bush is viewed as better able to deal with foreign policy.

Gene Sperling, an adviser to Kerry on economic matters, said a strategy in the St. Louis debate was to lay out elements of Kerry’s domestic programs in preparation for Arizona rather than using precious time to criticize Bush.

“There will be some people who say, “Why didn’t he just knock his socks off?’ But there are still some people who hadn’t heard specifics about health care, the economy,” he said.

Voters’ reaction to the St. Louis debate will determine not just how but where the campaign is waged in its final three weeks. Candidates in recent days have pared the original list of 17 or so swing states, judging from recent polls and the candidates’ advertising, The most recent polls suggest that the race remains the most competitive in Ohio, Florida, Wisconsin, New Hampshire, Iowa, Colorado and New Mexico. Both candidates planned to campaign in New Mexico on the way to the last debate in Arizona.