Newly minted Republican Senate nominee Joe Miller called for his party to unite following his upset victory over incumbent Sen. Lisa Murkowski in the Alaska primary, vowing to expand his lead in the polls over his Democratic opponent.

Despite tensions between the Tea Party-backed candidate and Republican Party leaders, National Republican Senatorial Committee Chairman John Cornyn endorsed Miller Tuesday night and pledged national support for his general election campaign.

Miller, in an interview with Fox News, cited the endorsement as a sign that fractures in the party would heal before November.

"I'm certain that we're going to have a unified front in the fall election," Miller said Wednesday.

The Fairbanks attorney shocked the political establishment after polls closed last week with Miller holding a slight edge over Murkowski. State election officials began counting absentee ballots Tuesday, but with Miller's lead staying above 1,200 votes, Murkowski conceded.

The contest had turned increasingly bitter over the past week as observers from both campaigns flocked to the ballot-counting sites across Alaska. Miller accused Murkowski and the NRSC of trying to skew the results; Murkowski's campaign called Miller "paranoid."

Democrats may see an opening to exploit any lingering divisions to build support for Democrat Scott McAdams, the mayor of Sitka.

Even before Murkowski conceded, Sen. Robert Menendez of New Jersey, chairman of the Democrats' campaign committee, said in an interview his organization might come into the state behind McAdams.

Any attempt to elect McAdams would involve gaining the support of independents, disappointed Murkowski supporters and other voters fearful that Miller's calls for cuts in government spending would hurt a state that has long benefited from federal largesse.

McAdams, a former commercial fisherman, was given little chance against Murkowski, and as of June 30 had raised less than $10,000.

But Democrats figure his chances are better against Miller, and they plan to present him as a moderate, rational alternative.

"Lisa Murkowski is a class act who always put Alaska first," McAdams said in a statement late Tuesday. "By contrast, lawyer Joe Miller ran an unfair, nasty campaign that didn't extend to Lisa Murkowski the respect she deserves."

The Associated Press contributed to this report.