A decorated Gulf War veteran was holding a narrow lead over Sen. Lisa Murkowski in the Alaska Republican Senate primary, as ballots continued to be counted Wednesday in what could shape up to be a stunning political upset. 

Polls taken before primary day had shown Murkowski, a two-term senator from an Alaska political dynasty, leading handily against the first-time candidate. But challenger Joe Miller insisted all along that the state's polling was unreliable -- as of Wednesday morning, Miller held a 2,000-vote lead. 

With 98 percent of precincts reporting, he had 51 percent and Murkowski had 49 percent. The number of uncounted absentee ballots, though, exceeded the number of votes separating the candidates. 

The Alaska race marked the second surprise from a Tea Party-backed candidate in Tuesday's elections. Health care executive Rick Scott earlier defeated Florida Attorney General Bill McCollum for that state's GOP gubernatorial nomination after polls also showed McCollum pulling away from Scott. 

Miller had the added help of an endorsement from former Alaska Gov. Sarah Palin, who has a history with the Murkowski family. Palin defeated Murkowski's father Frank in the 2006 gubernatorial primary. Though there was speculation over whether she might challenge Murkowski for her seat, Palin instead endorsed Miller after leaving the governor's office. 

Murkowski has proudly touted her seniority after eight years in office, and said her roles on the appropriations and energy committees put her in a strong position to ensure Alaskans' voices are heard. She denounced Miller for making what she considered deceptive statements about her votes and statements. 

But Miller, standing behind his words, sought to cast Murkowski as being too liberal and part of the problem in an out-of-control Washington. 

Miller told reporters he's trying to be realistic about the early results showing him slightly in the lead. He spoke to reporters at election central headquarters in Anchorage, where his supporters chanted "Miller Time!" and "Go Joe Go!" Miller joked on Twitter, "What's the moose hunting like in the Beltway?" 

Murkowski spokesman Steve Wackowski said the campaign remained upbeat about its chances, especially with votes in rural Alaska still coming in. More than 16,000 absentee ballots were mailed, and the state Division of Elections said it had received about 7,600 absentee-type ballots by Monday. They won't be counted until Aug. 31. 

"I can say we're still here waiting. That's what we're doing," Murkowski said shortly after midnight at her campaign headquarters. 

Asked if she conceding, she replied, "Absolutely not." 

After keeping a low profile for much of the race, Palin recorded a robocall for Miller in the final days of the campaign and touted him as a "man of the people" on her Facebook page. The former Alaska governor also repeated a claim that Murkowski had waffled on her position on repealing the federal health care overhaul -- claims the senator has called false. 

Palin has been on a losing streak as of late with her candidates faltering, and many were expecting similar results in Alaska with Murkowski holding such a name-recognition and fundraising advantage. 

Palin tweeted late Tuesday that she's "keeping fingers crossed" and "prayers upward" about the race. 

Murkowski has fought back against Miller and Palin's claims. A radio ad on the election's eve calls Miller out as twisting the truth about Murkowski's position on the federal health care overhaul. Miller has stood by his statements. 

"Alaskans deserve to know the honest truth," she said, "and they haven't gotten it from Miller." 

The race was disrupted when former Sen. Ted Stevens died in a plane crash, with both candidates briefly suspending their campaigning. 

Miller had the blessing of the tea party crowd. The national Tea Party Express reported spending at least $550,000 to help Miller. 

Murkowski was appointed to the Senate at the end of 2002 by her father and won her first term in 2004. 

The winner of the primary will face Democrat Scott McAdams. 

In Florida, Scott pulled out an upset late Tuesday by defeating the politically established attorney general. Scott spent millions on the race after entering late -- McCollum conceded early Wednesday morning but did not endorse his opponent. 

The Associated Press contributed to this report.