The stakes are high for the governor of Florida as his polling sags fewer than seven weeks out from the Iowa caucuses.Call it the “Debate Me Please” showdown.Ron DeSantis of Florida, 45, and Gavin Newsom of California, 56, two relatively youthful governors adept at seeking — and finding — the spotlight, will square off at 9 p.m. Eastern on Thursday in a nationally televised debate in Alpharetta, Ga., in suburban Atlanta. Both pleaded for this matchup, and now they have it.Each has an agenda, both near-term and further out, as well as political challenges that they hope to address during their 90-minute encounter. Mr. DeSantis, the Republican, needs to lift his campaign for president a week ahead of the fourth Republican primary debate and under seven weeks before the Iowa caucuses. Mr. Newsom, the Democrat, needs to lift the fortunes of his president, Joseph R. Biden Jr., and prove in the short run that he is a team player, and in the medium term that his appeal can reach beyond the liberal enclaves of the West Coast.With Donald J. Trump still holding wide leads in the Republicans’ 2024 nominating contests, and Mr. Biden resolute on standing for re-election, both men could also be eyeing the 2028 presidential race, though neither would admit it. They have presented themselves as the fresh, new avatars of their respective ideologies and, potentially, the future of their political parties. Now, after they have used each other as foils for years, the debate could offer a culmination to their long-running public feud.Here is what to watch.The higher stakes for DeSantisMr. DeSantis has much more riding on this moment than his verbal sparring partner.The first three Republican presidential debates featured jam-packed stages, some verbal brawling, often involving the 38-year-old entrepreneur Vivek Ramaswamy, and not a lot of Mr. DeSantis. Thursday night will be one-on-one, and with a friendly moderator, Sean Hannity, for the Republican on the stage.Mr. DeSantis’s poll numbers have sagged, leading him to seek exposure at every opportunity, including the debate against Mr. Newsom. Now Mr. DeSantis, who once preferred to ensconce himself in the friendly bubble of conservative media, has become almost a regular on mainstream broadcast networks.He has also repeatedly challenged his main rivals for the Republican nomination to debate him, hoping to generate momentum and attention, although his performances onstage so far have done little to change the dynamics of the race. But Mr. Trump has refused to appear at the G.O.P. debates, saying they were not worth his time given his lead in the polls. And former Gov. Nikki Haley of South Carolina, who has caught up with or overtaken Mr. DeSantis in many early-state polls and has been busy building support among influential Republican donors, declined his recent offer of a one-on-one matchup.Voters in Iowa go to the caucuses Jan. 15 to cast the first ballots of the primary season. Mr. DeSantis has nailed down the coveted endorsements of the state’s governor, Kim Reynolds, and an influential evangelical leader, Bob Vander Plaats. Now he has to win over more Republican voters if he hopes to catch Mr. Trump and buoy his campaign ahead of more difficult primaries in New Hampshire and South Carolina.There will not be a partisan audience to influence viewer perceptions, but Mr. Newsom’s camp fully expects Mr. Hannity to unlevel the playing field: “We’re under no illusions; this is going to be a two-on-one match with the ref in the bag for the home team,” said Nathan Click, a Newsom spokesman.If the moderator keeps the Democrat on the defensive over policy, Mr. DeSantis could use the 90 minutes on Fox to combat his awkward, remote and sometimes canned image. DeSantis supporters say it’s a moment for him to highlight the stakes for the Republican Party in a debate not over marginal policy differences between Republicans, like the primary debates, but over starkly different visions of the future. If he can best Mr. Newsom, he can bask in the victory of a unified party, if only for one night.“Ron DeSantis will take this responsibility seriously and looks forward to sharing the stark contrast between his vision to revive our nation and Newsom’s blueprint for failure,” said Mr. DeSantis’s campaign manager, James Uthmeier.A top Biden surrogate seizing the spotlightIn political circles, it goes without saying that California’s governor has his eyes on the highest office in the land.“It’s very obvious that he is running for president right now,” said Jessica Patterson, the chairwoman of the California Republican Party. “He elevates himself to a national level when he tries to punch up to Ron DeSantis. Every opportunity he gets to be on the national stage, he goes for it.”Maybe so, but as long as Mr. Biden is seeking re-election, Mr. Newsom’s job on that stage is to defend the president’s record. Nothing else would lift Mr. Newsom in the eyes of his own party more than his help keeping a Democrat in the White House next year — and Mr. Trump out.But to be a credible surrogate, Mr. Newsom cannot come off as an elite, West Coast liberal out of touch with the concerns of voters in key swing states far from California, like Pennsylvania, Michigan, Wisconsin and Georgia.Can Hannity keep the focus on policy?Mr. Hannity sees the showdown not as a stand-in for a presidential debate but as a chance for the governors of the first and third largest states in the nation to defend and showcase the very different policies governing those states.“I think both governors really have an opportunity to present their political philosophy and ideology, why they govern the way they do,” he said in an interview.They would have much to discuss: Florida’s low-tax, growing economy versus California’s dominance in fields like technology and electric vehicles but struggles against Republican states poaching its businesses; university systems with divergent approaches to political speech and influence; California’s hands-on approach to climate change, including an eventual ban on internal combustion engines, versus Florida’s laissez-faire attitude even as it is battered by stronger, more frequent hurricanes and coastal flooding.Mr. DeSantis has relished talking up his record in Florida. He often brags about how many California residents are moving to Florida, claiming that Mr. Newsom’s “leftist” policies are responsible. Mr. DeSantis once said that Mr. Newsom had treated Californians like “peasants” during the coronavirus pandemic. He filmed a campaign ad in San Francisco that painted the city as a kind of dystopia, with Mr. DeSantis saying he had seen people using drugs and “defecating on the street.”Mr. Newsom has also not held back. During Mr. DeSantis’s re-election campaign, he ran a pointed ad on Florida airwaves criticizing Mr. DeSantis’s policies and recently ran another attacking the six-week abortion ban signed by the Florida governor. He has called Mr. DeSantis “weak” and “undisciplined” and said he would get “crushed” by Mr. Trump in the G.O.P. primary. After Mr. DeSantis sent planeloads of migrants from the southern border to Sacramento this year, Mr. Newsom suggested his Florida counterpart could face kidnapping charges, calling him a “small, pathetic man.”Mr. Newsom still sees the evening as “a way to showcase and put more scrutiny on Mr. DeSantis’s brand of authoritarianism,” Mr. Click said.But both men have said their more pressing objective for this debate is the White House, not the state house.“We’re focused on defending the president and contrasting the president’s record with Ron DeSantis’s record of taking away fundamental freedoms that we have come to take for granted over the last 50 years,” Mr. Click said, tallying off abortion, free speech and the right to vote.Location, location, locationThe Newsom camp has made much of the California governor’s willingness to venture into hostile territory and bring his message to Republican voters. And just a decade ago, the northern reaches of Fulton County, Ga., where the debate is being held, qualified as such.Not anymore. Most of North Fulton has turned Democratic in the last eight years, as its citizenry has diversified and many suburban Republicans have recoiled at the party’s direction under the leadership of Mr. Trump. Mr. Trump eked out a win in the ZIP code where the debate will be held, though his margin slipped by nearly 5 percentage points. But all around that 30005 ZIP code are blue stretches, a testament to Georgia’s arrival on the national stage as a true presidential battlefield.Both camps said they wanted the debate in Georgia (Mr. DeSantis will be campaigning on Friday in South Carolina next door). Fox News chose the venue, a battleground within a battleground.Adam Nagourney More