Liz Cheney is mailing instructions to Democrats on how to change parties and vote for her in Wyoming's GOP primary

• Rep. Liz Cheney has mailed instructions to Wyoming Democrats on how to switch parties to vote for her.
• Cheney is facing a tough reelection challenge against a Trump-backed primary opponent.
• The Wyoming Republican primary takes place on August 16.

As Rep. Liz Cheney faces a tough reelection battle in Wyoming, she's turning to Democrats in her home state to help her chances in the August 16 Republican primary.

Cheney's campaign has mailed instructions to Wyoming Democrats on how to change their party affiliation to vote for the incumbent congresswoman, The New York Times reported on Thursday. Under Wyoming law, voters must be registered as a Democrat or a Republican in order to vote in that party's primary election. 

The instructions, also listed on Cheney's campaign website, direct voters to fill out a registration form and submit it to their county clerk's office at least two weeks before the primary. Voters may also change their party affiliation at the polls on primary day or when they request an absentee ballot. 

"Liz is proud to represent all Wyomingites and is working hard to earn every vote," Jeremy Adler, a campaign spokesperson, told Insider in a statement on Thursday. 

This call comes as some Democrats in the red state have expressed support for Cheney's defiance of former President Donald Trump and plan to vote for her reelection. Though Republicans are a majority in the state, it's not unusual for candidates to reach out to Democrats during campaign season to boost their election bids. Studies on voter data in the state have shown that party-switch voters have not made a difference in past elections.

"There'll be Democrats who change their affiliation to vote Republican in the primary, and that's not necessarily an uncommon thing to happen in Wyoming," Joe Barbuto, chair of the Wyoming Democratic Party, told Insider last month. "You'll probably see more than usual going out there and voting for Liz Cheney, but not enough I don't think to save her, if she's in fact in trouble."

Cheney, once the No. 3 Republican in the House and a shoo-in for reelection in Wyoming, faces an uphill battle as Trump and his allies seek to oust her from Congress. Trump has endorsed Harriet Hageman, a local attorney and former Republican National Committeewoman, to defeat Cheney, his toughest Republican critic in Congress. Last month, Trump repeatedly slammed Cheney at a Hageman campaign rally in Wyoming, where his supporters pledged their loyalty to the former president.

The primary widely represents a test of Trump's influence over the Republican Party. There has been scant polling on the race so far. One survey conducted by Club for Growth, a political action committee that supports Hageman, shows her in the lead. 

As part of his push to drive out Cheney, Trump and his allies endorsed an effort to change Wyoming laws to prevent voters from switching their party affiliation on the day of the primary election. Wyoming state lawmakers rejected such a bill in March.

Despite Trump's attacks on Cheney, she has received support from high-profile Republicans, including former House Speaker Paul Ryan and President George W. Bush, who have fundraised on her behalf. A slew of Republican state and local officials in Wyoming have also backed Cheney's reelection bid. The congresswoman has framed her campaign around upholding the Constitution and the rule of law, and defending Wyoming against the Biden administration's policies.