PHOENIX – President Bush and John Kerry get their last chance to challenge each other face to face in front of a nationwide audience tonight, a moment that could allow one to open a lead or solidify the contest as a dead heat going into the campaign’s final weeks.

The audience for their third and final debate is likely to be in the tens of millions, many of them swing voters who haven’t committed to either major party candidate.

A gaffe or poor performance could turn some away from one candidate. Bush lost ground with a weak showing in the first debate on national security, which was his political strength. A strong performance by both men, as happened in the second debate, could reinforce each’s base of support and keep the contest close.

The new element tonight is that the debate will focus entirely on domestic issues including the economy, education, health care and taxes. If the candidates’ stump speeches and performances in previous debates are any indication, odds are high that at some point each man will misstate facts, distort his rival’s record or otherwise mischaracterize the truth.

Here’s a viewers’ guide:

•Deficit. Both Kerry and Bush promise to halve the federal deficit over the next four years. But the Concord Coalition, a bipartisan deficit-watchdog group, says both candidates have proposed either tax cuts or spending increases that will add to the deficit rather than reduce it.

Both Kerry and Bush say their domestic initiatives will spur the economy and that will generate more tax revenue and reduce the deficit. But few experts buy it. “The bottom line,” the Concord Coalition says, “is that neither candidate has produced a credible set of numbers to back up his deficit-reduction rhetoric.”

•Jobs I. This is one of the most fact-challenged topics in the campaign. Bush argues that the economy is creating new jobs vigorously and is poised to make a strong recovery. While job growth has been stronger over the past 14 months, the latest numbers released by the administration fall short of what’s needed to reduce unemployment. Most analysts say the economy must create 150,000 jobs a month to keep up with population growth and more than that to reduce unemployment. Last week, the administration announced that fewer than 100,000 jobs had been created in September, the fourth straight month of tepid job growth.

•Jobs II. Kerry lately has been more careful to assert that during the Bush administration, 1.6 million “private sector jobs have been lost.” Kerry used to omit “private sector,” but that’s where the job losses are highest. Counting government jobs such as teachers, police officers, firefighters and federal government workers, the lost-jobs number is smaller – fewer than 900,000. Either way, when Kerry asserts that Bush will be “the first president in 72 years to lose jobs” on his watch, he will be correct – although when Bush replies that he inherited an economy sliding into recession, so will he.

•Health care. Lately, Bush has been saying that Kerry would “put big government in charge” of health care. Well, on the one hand, Kerry would permit more Americans to avail themselves of Medicare and Medicaid. But the foundation of his health-insurance plan relies on maintaining current employer-based plans. Kerry would have the government assume catastrophic costs of health care, easing the burden on businesses and reducing their cost of insurance. Some experts predict that Kerry also would increase regulations on employers and insurers, which gives Bush’s charge some support.

•Taxes. Bush says Kerry will raise taxes to pay for all his spending programs. Kerry insists he won’t, but his proposals beg the question, “Where will the money come from?” Kerry promises to expand health care at a cost of $650 billion over 10 years, by Kerry staff estimates. Some analysts have placed the cost at $1.5 trillion. Kerry has said he would pay for it by increasing taxes on the wealthiest 2 percent of taxpayers. That would generate about $860 billion, according to Kerry staff estimates. But Kerry has also proposed spending increases in education and homeland security. Kerry has said he would cut his spending programs if their costs were too high and, at the last debate, vowed he would not raise taxes on the middle class.

•Medicare. Kerry has been blaming President Bush for next year’s scheduled 17 percent increase in Medicare premiums. But Bush can hardly be held solely responsible; Congress went along, too. Slightly more than half of the increase is due to Medicare changes that Bush pushed through Congress as part of the new prescription drug law. Kerry was absent when that measure passed. Kerry said the administration could have included more cost-containment measures. But the rest of the increase is due to rising costs of health care, increased use of Medicare services and other factors.

•Abortion. George Bush opposes abortion. John Kerry supports the 1973 Roe v. Wade Supreme Court decision that protects abortion rights. Bush has criticized Kerry for voting against a ban on an abortion procedure that its opponents call “partial birth.” Kerry has said that as a Catholic, he abides by his church’s teachings against abortion, but says he does not want to impose his church’s morality on the U.S. public, most of whom do not share his religion. He also has said that he voted against banning the abortion procedure because it did not contain any exception to protect the health of the mother.

•Gay marriage. President Bush wants a constitutional amendment to ban gay marriage. An effort in the House of Representatives to begin the constitutional amendment process failed last month. In 1996, when Congress voted to bar federal recognition of same-sex marriage, Kerry was one of 14 senators to vote against the legislation. But Kerry has since said he opposes gay marriage and supports civil unions.

•Kerry as liberal. Count on the president to voice some variation of his standard stump line: “My opponent is a tax-and-spend liberal. I’m a compassionate conservative.” Kerry has, in fact, usually voted with the liberal wing of his party, but his overall Senate record puts him in the mainstream of Senate Democrats. National Journal magazine ranked him as having the most liberal record in 2003, but Kerry only cast votes in the most partisan roll calls last year, missing most other votes while campaigning for the presidency.

Kerry makes a point of dismissing Bush’s charges by saying he doesn’t believe in such labels. Yet, as recently as last week, he was criticizing Bush for hewing to an “extreme right-wing ideology” for limiting federal funding for research on stem cells.