Kari Lake opened her Senate run in Arizona showing every intention of shedding the trappings of the Trumpism that made her a star in conservative circles but cost her the governor’s race two years ago: unfounded claims of election fraud, ruthless attacks on fellow Republicans and obsequious tributes to former President Donald J. Trump.

Ms. Lake, a former television anchor, has reached out to her critics. She has sought to appeal to the Republican establishment in ways that Mr. Trump has not, framing his Make America Great Again movement as a natural evolution of Reaganism, which attracted legions of voters to the party more 40 years ago. And she has moderated her message on abortion, opposing a federal ban on the procedure she once called “the ultimate sin.”

But after six months as a Senate candidate, she is struggling to walk away from the controversial positions that have turned off independents and alienated potential allies, lashing out in ways that Republicans now backing her campaign have warned will result in another defeat.

At a campaign event last week in Cave Creek, Ariz., she announced plans to continue her legal challenges to her 2022 election loss, castigated Republicans as cowards who did not support her fight and claimed, without proof, that Democrats were orchestrating illicit voting schemes involving undocumented immigrants.

“That’s the only way they can win — with illegals voting,” Ms. Lake said.

Ms. Lake built a national political persona in remarkably short order with applause lines that electrified every corner of MAGA Nation. Now, in her second high-profile battleground campaign in as many years, her attempt to temper her approach enough to win a Senate seat is proving to be a difficult task, even for someone with communication skills polished after decades in the local TV news business.