LOS ANGELES — Arizona Sen. John McCain, who surrendered his maverick image to fend off a stiff conservative challenge, romped to the Republican nomination for a fifth term Tuesday, making a resounding comeback from his loss in the 2008 presidential campaign.

In Florida, Democratic Rep. Kendrick Meek fended off a multimillion-dollar onslaught to easily capture the U.S. Senate nomination over billionaire Jeff Greene. On the Republican side, free-spending businessman Rick Scott narrowly defeated Attorney General Bill McCollum for the gubernatorial nod.

The two Florida contests amounted to a split decision on the overriding theme of Tuesday’s primaries: insurgency vs. the political establishment, set against a backdrop of broad economic anxiety and widespread unhappiness with President Barack Obama and both major parties.

Elsewhere, in Alaska, GOP Sen. Lisa Murkowski was heavily favored to defeat attorney Joe Miller, who ran with support from the “”tea party”” movement and former Gov. Sarah Palin. Voters in Vermont and Oklahoma also went to the polls to decide gubernatorial and congressional races.

McCain seemed destined to face one of his toughest re-election fights ever, after virtually ignoring his home state to make two tries at the presidency. The four-term senator has never been well liked or completely trusted by Arizona’s right wing. By contrast, his main opponent, former Rep. J.D. Hayworth, enjoyed a conservative following from his congressional days crusading against illegal immigration and, more recently, as a Phoenix talk-radio host.

McCain, campaigning harder in Arizona than he had in years, shifted rightward on a number of issues, including immigration reform, climate change and the 2008 Wall Street bailout. He spent more than $20 million and used his enormous financial edge to bombard Hayworth with a relentless series of attacks; one of the most damaging used footage from a 2007 infomercial in which Hayworth touted “”free money”” to be had from the federal government. Strategists for McCain dubbed him “”J.D. Huckster.””

Hayworth accused McCain of an election-year conversion — he called himself “”the consistent conservative”” — and scorning McCain’s presidential ambitions. But Hayworth’s background, 12 years on Capitol Hill and an association with the imprisoned ex-lobbyist Jack Abramoff, made him a less-than-ideal messenger.

In claiming victory Tuesday night, McCain sounded as though he was still running against Obama. He predicted Republicans would win the House and Senate in November and said, “”When we do, we will stop the out-of-control spending and tax increases and repeal and replace Obamacare…We will secure our borders, defend our nation and bring our troops home from Afghanistan with honor and victory.””

McCain is a heavy favorite for re-election. Also in Arizona, Gov. Jan Brewer, who signed into law the state’s tough crackdown on illegal immigrants, won the GOP nomination and will face Democratic Attorney General Terry Goddard in the fall.

In Florida, political novice Greene poured millions into attack ads, portraying Meek as a corrupt Washington insider. Meek responded in kind. Greene’s business background and picaresque personal life — his intimates include boxer Mike Tyson and Hollywood madam Heidi Fleiss — offered plenty of fodder.

“”It shows Floridians that even when we run into a wall, we find a way to get around it, or over it, or through it,”” Meek told supporters in Hollywood, Fla.

The back-and-forth, however, did little to help Meek’s image. Polls show the Miami congressman trailing Republican Marco Rubio and Gov. Charlie Crist, who quit the GOP to run as an independent, in his bid to be Florida’s first black senator.

Scott and McCollum spent in excess of $50 million trashing each other in the governor’s race. Scott, a first-time candidate, attacked McCollum as a career politician and linked him to the state’s ex-GOP chairman, who has been indicted for allegedly misusing party funds. McCollum accused Scott of “”ripping off taxpayers”” as head of health-care giant Columbia/HCA, which was fined for committing major Medicare fraud under his watch.

The mud-heaving seemed to most benefit the Democratic nominee, chief financial officer Alex Sink, whose first TV ad criticized Republicans for bickering instead of addressing Florida’s problems.

In Alaska, Murkowski enjoyed a big financial edge over Miller, a lawyer in Fairbanks. The Tea Party Express spent hundreds of thousands of dollars on ads assailing Murkowski as insufficiently conservative and promoting Palin’s endorsement.

It is not clear, however, her support was much help. Palin’s popularity plunged in Alaska after she joined the national GOP ticket, and fell again when she left office with 18 months remaining in her term.

“”The fact that Sarah Palin is rooting for him is a negative in my mind,”” said Valerie Barber, a university research professor and political independent, who backed Palin for governor but soured on her as vice presidential nominee. “”I think she speaks out without really thinking about things. I think she’s a little too antagonistic. And I just don’t think she’s very smart.””