ANCHORAGE — A tea party attempt to overcome a mainstream Republican appeared to be coming up short in Alaska as former state Attorney General Dan Sullivan took a primary lead in the fight to be the GOP candidate to take on U.S. Sen. Mark Begich in the fall.

Sullivan entered the primary the presumed front-runner, with the backing of national GOP powerbrokers and a huge cash advantage over his rivals.

Sullivan held an edge Tuesday night over tea party favorite Joe Miller, who made a late push reminiscent to his 2010 primary upset of U.S. Sen. Lisa Murkowski.

Lt. Gov. Mead Treadwell, meanwhile, was in third.

With 67 percent of precincts reporting, Sullivan led with 40 percent of the vote to Miller’s 32 percent. Treadwell collected 25 percent of Republican ballots.

The Republicans were vying to face Begich, who won his primary easily after facing no real threat.

The Alaska GOP Senate race mirrors national trends, with tea party conservatives trying to knock out mainstream Republicans.

Sullivan, who also had the support of Karl Rove and groups like Club for Growth, was considered the front-runner early on in part due to his fundraising prowess, which has rivaled that of Begich. Roughly $4 million in attacks have been run against Sullivan by a pro-Begich super PAC, with some of the knocks against him over his residency — a big deal in Alaska.

Sullivan is from Ohio, but his wife is from Alaska and his roots here date to the 1990s. He left the state in 2002 for stints in George W. Bush’s administration and overseas with the military, before returning in 2009 and being appointed attorney general by Palin.

Tuesday morning, Sullivan was out with supporters — including his wife, three teenage daughters and niece — waving signs along a busy Anchorage street and looking relaxed.

“We’ve got to win today, but as you know, it’s not like I’m going to be new to attack ads, OK?” he said, noting how Democrats and the super PAC Put Alaska First went after him. “That’s because they’re afraid, they fear me.”

Sullivan spent the last few days leading up to the primary covering hundreds of miles in an RV; he skipped the last debate to be broadcast statewide to focus on door-to-door campaigning.

“I’m proud of the campaign we ran,” he said, adding: “We have not left any stone unturned.”

Palin, who has little to do with state-level politics since resigning in 2009 and becoming a paid contributor for Fox News, re-emerged to support an oil tax referendum that also is on the ballot — if successful, it would restore the tax system she championed as governor — and to endorse Miller.

Miller was largely considered a wild card and long shot, but he was running a race that smacked of 2010. That year, he upset Murkowski in the GOP primary, but wound up losing to her in the general election after she ran a write-in campaign.

He had a network of loyal supporters, attention from conservative talk radio hosts and endorsements from anti-abortion and tea party-style groups. While he exuded confidence in the race’s final days, Miller said late Tuesday afternoon, after being greeted warmly by sign-waving supporters along a busy Anchorage street, that he did all he could do.

“We’ve left nothing on the table,” he said, noting the support he’s received has been “phenomenal.”

Supporter Amy Walker of Palmer, who was sign-waving for Miller, said she didn’t think about voting for anyone else, calling Miller a “champion for liberty.”

Treadwell had cast himself as the “electable” conservative, in contrast with Miller. Treadwell also played up his decades-long ties to the state, as opposed to Sullivan. He argued his knowledge of Alaska issues, from fisheries to aviation, made him the strongest candidate to challenge Begich. His endorsements included four-time Iditarod champ Martin Buser and astronaut Buzz Aldrin, which came near the end of the race.

Campaign manager Peter Christensen, out sign-waving Tuesday morning across the street from a clutch of Miller supporters, said some people don’t start to follow a race until it’s nearly over. He said endorsements tend to work that way, too.

Treadwell, who struggled to race money after Sullivan jumped in, said he was proud of the race he ran and would do what he could to bring the party together after the bruising primary.

“In terms of the money issue, whatever happens tonight, the fact that we were in contention, solidly in contention, being outspent 4-to-1 by huge outside money, is significant,” he said. “And I am very grateful to Alaskans who respected our record and respected our positions and respected our ability.”

Sullivan raised about four times as much as Treadwell, drawing from donors nationally.

Alaska voters also advanced Republican Gov. Sean Parnell and Democratic gubernatorial candidate Byron Mallott to the general election, where independent candidate Bill Walker will await.

In the race for U.S. House, Republican Rep. Don Young, who is seeking a 22nd term, and 29-year-old political upstart Forrest Dunbar, a Democrat, both won their primaries.

A ballot measure on whether to repeal a new tax on oil companies operating in the state remained too close to call.

Another western state, Wyoming, also held its primary election Tuesday, as U.S. Sen. Mike Enzi and Rep. Cynthia Lummis defeated lesser-known challengers from within the Republican Party.