Sen. Lisa MurkowskiLisa Ann MurkowskiEmboldened Trump takes aim at GOP foes The Hill's 12:30 Report - Presented by Facebook - DC prepares for Saturday of festivals & Jan. 6 demonstration Republican leaders misjudged Jan. 6 committee MORE received a warm welcome from fellow Senators on the Senate floor Monday and congratulations from National Republican Senate Campaign Chairman John CornynJohn CornynDemocrats make case to Senate parliamentarian for 8 million green cards Democrats to make pitch Friday for pathway to citizenship in spending bill Without major changes, more Americans could be victims of online crime MORE.

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Ballots are still being counted in Murkowski's write-in battle against Republican nominee Joe Miller, but the senator's camp appears confident she will come out on top.

Elections officials continued the write-in ballot count Monday and Murkowski is still winning close to 90 percent of those votes unchallenged. That puts her on a path to eclipse Miller's total by a few thousand votes once the counting concludes. Miller was backed by the Tea Party and defeated Murkowski in the August GOP primary. She ran as a write-in candidate in the general election.

The senator received congratulations from several members, both Republican and Democrat, Monday on hand for the swearing in of Sens. Chris CoonsChris Andrew CoonsBiden threatens more sanctions on Ethiopia, Eritrea over Tigray conflict Senate Democrats to Garland: 'It's time to end the federal death penalty' Hillicon Valley: Cryptocurrency amendment blocked in Senate | Dems press Facebook over suspension of researchers' accounts | Thousands push back against Apple plan to scan US iPhones for child sexual abuse images MORE (D-Del.) and Joe ManchinJoe ManchinBriahna Joy Gray: Push toward major social spending amid pandemic was 'short-lived' Overnight Energy & Environment — Presented by Climate Power — Emissions heading toward pre-pandemic levels Biden discusses agenda with Schumer, Pelosi ahead of pivotal week MORE (D-W.Va.).

Asked about her exchange with Cornyn, Murkowski said, "He said 'congratulations' as everybody else has, and what I tell everybody is, 'Well, it's not over yet,'" Murkowski said. "We still have more votes to count. I haven't had a sip of champagne yet."

Appearing upbeat and confident, Murkowski said she hopes to have some final news on the ballot count by Wednesday.

Cornyn and the NRSC backed Miller in the general election and have aided his ballot count efforts, but some Miller supporters, including Sen. Jim DeMint (R-S.C.) have questioned whether the national party is fully committed to Miller.

DeMint, a staunch opponent of Murkowski, was not on the floor Monday and Murkowski said she has not seen or spoken to him since her return to Washington.