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(CNN) -- Sen. Lisa Murkowski's bid to become only the second person to win a write-in campaign for U.S. Senate appeared on track in Alaska early Wednesday, with write-in candidates leading a Tea Party-backed Republican who beat her in a primary.

But even if the write-ins remained ahead of Republican nominee Joe Miller and Democratic candidate Scott McAdams, the outcome of Alaska's Tuesday general election apparently wouldn't be known for days, because officials need to determine which write-in votes actually went to Murkowski.

"We are in the process of making history," Murkowski, who is seeking a second full term, said early Wednesday.

Although Murkowski told supporters in Anchorage, Alaska, late Tuesday that the outcome wasn't yet known, she was clearly optimistic about her chances.

"They said you can't do it, [that] you can't win a write-in campaign, not in Alaska, not anywhere. They said we can't do it," Murkowski said. "Do they know Alaska?"

With 73 percent of precincts reporting, write-in candidates as a group had 40 percent of the vote, with Miller collecting 35 percent and McAdams 24 percent, according to an unofficial count from The Associated Press.

Alaska had dozens of eligible write-in candidates. Officials didn't plan to read the write-in votes until November 18, in part because they need to wait for mail-in votes, according to the state's election division.

With a victory, Murkowski would avenge her August primary loss to Miller in the latest chapter of a feud between her and his main backers, including the Tea Party Express and former Alaska Gov. Sarah Palin.

She told CNN Wednesday morning that, although she wasn't her party's nominee, she intended to caucus with Republicans should she win.

"This is about a can-do people," Murkowski told her supporters late Tuesday. "When they tell us we can't do something, what do we do? We stand up just a little bit straighter, just a little bit taller, and we take it on."

"We're doing it for Alaska, for our kids, for our families, for the people in this state, because this is the right thing to do," she added.

The Tea Party Express, a national Tea Party organization based in Sacramento, California, endorsed Miller earlier this summer and spent nearly $600,000 during the primary campaign to help him defeat Murkowski.

The primary race was so close, with Miller eventually garnering 51 percent, that Murkowski didn't concede until a week after the vote, while absentee ballots were still being counted. She announced a write-in candidacy in September.

Miller backers accused her of going back on her word to support the winner of the GOP primary. Murkowski's campaign took aim at the California-based Tea Party Express, accusing it of trying to meddle in Alaska and steal the seat.

The race also was another entanglement between the Murkowski family and Palin, the 2008 Republican vice presidential nominee who endorsed Miller.

Murkowski was appointed to her post in 2002 by her father, Frank Murkowski, who had given up the seat to become governor. In 2006, Palin defeated the elder Murkowski in a gubernatorial primary.

Miller, an attorney and former U.S. Army officer, was fighting against controversies in the race's last few weeks, including allegations that he was disciplined years ago for improperly using government computers for private use and then lied about it. Later, Miller's security detail -- two active-duty soldiers hired by a third party working for Miller -- handcuffed a journalist trying to question him. The Army is investigating the soldiers' involvement.

During a debate last month, Murkowski took aim at Miller, a U.S. Military Academy graduate, asking him, "What would your instructors, what would your classmates at West Point say about how well you have lived up to your code of honor?"

At a subsequent rally, Palin came to Miller's defense.

"I find it shameful .. this establishment part politician, shamefully used Joe Miller's honorable military service as a means to attack him," Palin said.

McAdams, the mayor of Sitka, Alaska, was expected to be helped by having Murkowski and Miller share GOP votes, but he always faced long odds in the heavily Republican state.

Strom Thurmond of South Carolina was the first to pull off a write-in election to the Senate, in 1954.

CNN's Drew Griffin, Paul Steinhauser, Kathleen Johnston and Alexander Mooney contributed to this report.