Sen. Lisa Murkowski appears likely to be certified the winner of her drawn-out re-election bid against fellow Republican Joe Miller before the new Congress begins in January.

A state superior court judge ruled last week against Miller’s complaint regarding Alaska’s methods for counting write-in ballots, but Miller appealed the ruling to the state Supreme Court, where arguments will begin Friday.

Meanwhile, U.S. District Judge Ralph Beistline said Tuesday that one of the candidates should be installed as Senator by Jan. 3, even if that person must be replaced after all legal disputes are resolved, the Associated Press reported. 

Beistline, who issued a stay on the certification of the election until the state courts complete their review, said Miller would be allowed to take his case to federal court if he loses his appeal, the AP reported.

Murkowski led by more than 10,000 votes at the end of ballot counting, but that lead would shrink to about 2,000 votes if Miller’s challenges to ballots with misspellings and other errors are upheld. The lower court ruled against his complaint last week, stating that the state’s policy of following voter intent was a common-sense method to use.

Miller’s campaign wants a recount of all 255,000 votes, saying there were thousands of inaccuracies and inconsistencies in the original count.

Republicans in Alaska and Washington, D.C., have called on Miller to concede, while the National Republican Senatorial Committee is letting the state sort it out.