Republican Senate candidate Kari Lake repeatedly reminded viewers Wednesday of her three-decade career on Arizona television, looking to harness the intimate connection she built with voters and overcome Democrat Ruben Gallego's portrayal of her as a liar in the only debate of the closely-watched race.

The Arizona race is one of a handful that will determine which party controls the U.S. Senate, where Democrats are fighting an uphill battle to retain their slim majority. The winner will replace independent Sen. Kyrsten Sinema, who was elected as a Democrat in 2018 but left the party after her relationship with the party's base ruptured.

Both candidates are working to win over a small share of Republicans and conservative independents who are open to splitting their vote between the parties. This group has been instrumental in the rise of Democrats in Arizona, which has transitioned from a Republican stronghold to a battleground state over the past decade.

Lake's comfort and polish in front of the camera stood in contrast to Gallego, a military veteran who occasionally tripped on his words. The hourlong forum, at times caustic and personal, highlighted big differences on immigration, border security, abortion and taxes.

"Arizona, it's so good to be back with you, where our relationship began, right here in your home," Lake said to start the debate.

She accused Gallego of undergoing an "extreme makeover" to downplay his progressive record in the U.S. House and sought to tie him to disorder on the U.S.-Mexico border.

Gallego called Lake a liar, pointing to her discredited claim that she won the 2022 race for governor.

"She will do anything and say anything to gain power, including lying," Gallego said.

Lake, who became a darling of the populist right after leaving her career as a local television news anchor, has tried but struggled to redefine herself since losing in 2022.

Gallego, who represents largely Latino areas of Phoenix, has used his financial advantage over Lake to run ads playing up his military service and up-by-the-bootstraps personal story rather than his progressive record in the House.

The debate, which aired live on most television stations across the state, presented Lake with a chance to reset a race where polls and observers suggest she's modestly trailing. For Gallego, it was an opportunity to introduce himself to the voters who still don't know him.

The first half of the debate was devoted to immigration and border security, the issues Lake has put at the center of her pitch to voters. She pointed to Gallego's prior comments critical of a border wall, tied him to President Biden's border policies and said he supports "open borders" and "voted against border security every step of the way."

"Your votes on the border have empowered the cartels," she said, calling illegal border crossings an "invasion." She also alleged Gallego "wants" undocument immigrants to vote, a claim that CBS Phoenix affiliate KPHO fact-checked as "false."

Lake also alleged that hospitals have had to close down due to border crossings, which KPHO also ranked as false. The future of five hospitals in Arizona is in doubt when the owner of Steward Health Care filed for bankruptcy, according to KPHO, after allegations of corporate mismanagement. A year-and-a-half-long investigation by CBS News has documented how private equity and other investor groups have siphoned hundreds of millions of dollars from community hospitals with devastating public health consequences.

Gallego pushed back, saying borders are necessary and walls are an important part of security, but only if coupled with sufficient manpower and technology. He faulted Lake for opposing a bipartisan border security bill agreed to by Mr. Biden and key lawmakers, which died after former President Donald Trump urged Republicans to oppose it.

"You've been to Mar-a-Lago more than you've been to the border," Gallego said, calling attention to Lake's frequent trips to Trump's resort in south Florida.

Lake pushed Gallego to support deporting everyone living in the country illegally. He pushed her to oppose deporting "dreamers," a group of immigrants brought to the country as children. They did not agree on either.

They have fought to focus voters on the issue most favorable to them. For Lake, that's the border.

For Gallego, it's abortion rights after a state Supreme Court ruling outlawed virtually all abortions until the Legislature rolled the ban back to after 15 weeks of pregnancy. Lake has spoken favorably of stricter limits.

"She said she was thrilled that Roe was overturned," Gallego said. "And so, do we want politicians like Kari Lake to be involved in these very, very difficult decisions when they should be left to the woman and the family?"

Lake said she would not vote for a federal abortion ban and pointed to a ballot measure that will be presented to Arizona voters next month.

"We have the choice as Arizonans to decide what our abortion law will be," Lake said. "It's going to be up to us."

Lake is an unflinching supporter of Trump and his lie that he lost the 2020 election because of fraud. She has never conceded she lost her own 2022 race for governor, and continued to fight the outcome in court even after launching her Senate campaign. Separately, she's tried and failed to persuade courts, including the U.S. Supreme Court earlier this year, to outlaw the use of electronic voting machines.

She's also highlighted Gallego's 2016 divorce from Kate Gallego, who is now the mayor of Phoenix. Noting the marriage ended weeks before the couple's son was born, Lake says Gallego abandoned his wife while she was pregnant. Kate Gallego has endorsed her ex-husband and campaigned with him as recently as last week.

"Look at his character and his background," Lake said Wednesday.

The son of immigrants from Mexico and Colombia, Gallego was raised in Chicago by a single mother and eventually accepted to Harvard University. He enlisted in the U.S. Marine Corps Reserve while he was on a break from Harvard. He fought in Iraq in 2005 in a unit that sustained heavy casualties, including the death of his best friend.

He pointed repeatedly to his military service during the debate.