Cheney, an outspoken Trump critic and member of the US House Select Committee on the events of January 6, 2021, faces a primary challenge by Harriet Hageman, a natural resources attorney and former Republican National Committeewoman who is endorsed by Trump.
Polls indicate Hageman has a double-digit lead despite having raised only $4 million for her campaign compared to Cheney's $15 million. Cheney also received endorsements from Republican notables, including former US House Speaker Paul Ryan and former President George W. Bush.
Trump has frequently criticized Cheney and her work on the January 6 Committee, calling her a “warmongering and despicable human being” who is “hated by the great people of Wyoming.”
Analysts have suggested that the only way for Cheney to overcome Hageman's lead is if significant number of Democrats and Independents join the Republican primary and vote for her, adding that the chances for such a development are scant.
Cheney is daughter to former US Vice President Richard “Dick” Cheney and served in the George W. Bush administration as Deputy Assistant Secretary of State for Near Eastern Affairs, which covers diplomatic operations in North Africa and the Middle East.
Murkowski faces primary challenges by 18 other candidates, out of whom the top four will move on the ballot for the general elections in November. Trump backed candidate Kelly Tshibaka, a so-called moderate who has clashed with establishment Republicans like Murkowski.
Tshibaka has served in positions, including as special assistant to the Justice Department Inspector General and Commissioner of the Alaska Department of Administration.
Murkowski voted to convict Trump in the impeachment trial that followed the 6 January events at the US Capitol. Trump was ultimately acquitted.
Alaska is also holding on Tuesday a special election to determine who will serve for the remainder of the late US Congresswoman Don Young’s term. The three candidates running for office include former Alaska Governor Sarah Palin, fellow Alaska Republican Nichola Begich and former Alaska House Democrat Mary Peltola.
Analysts are watching the outcomes of the Republican primaries featuring pro-Trump challengers as potential early indicators of where the political party is moving ahead of both the midterm elections and the 2024 presidential race.