In an interview on Friday morning with KTAR 92.3 FM, Woods, a Republican-turned-Democrat who has become a critic of President Donald Trump, said that if he ran for the Senate seat, he could expect to face "a big-time, expensive, competitive primary."
He has "zero interest" in fighting Democrats, Woods told hosts Bruce St. James and Pamela Hughes. “The Democrats are not the problem right now," Woods added.
Woods served as Arizona's top law enforcement official from 1991 to 1999 as a Republican. Before his run for attorney general, at the age of 28, Woods became John McCain's first chief of staff when the late senator was a congressman.
He switched his party affiliation to officially register as a Democrat last November, and endorsed Kyrsten Sinema in her successful 2018 campaign against McSally for retiring senator Jeff Flake's seat.
In December, Arizona Governor Doug Ducey appointed McSally to the Senate anyway to fill the seat left vacant by McCain.
McSally must run again next year to retain the seat for the last two years of McCain's term, and then again in 2022 if she wants to clinch a full six-year term of her own.
Woods said his ambition was not to become a senator, but to serve as a counterweight to Trump and the president's allies.
"On a daily basis, he proves in my mind that he’s unfit to be president," Woods said on KTAR. "And so, No. 1 goal is we need to see that he’s not president anymore in the next election; No. 2 goal is we need to get rid of the Trump enablers, of which Martha McSally is one.”
Woods told the hosts that McCain's death motivated him to consider running for public office again. In an op-ed for the Arizona Republic last fall memorializing McCain, Woods wrote that the Republican Party has abandoned its moral authority and made it impossible to change the party from within.
"If I believe that our country is in perilous times, what is my responsibility as a citizen to do something about it? I have to do more, that much is clear. But does that mean I have to run for office again, this time for my mentor John McCain’s seat in the United States Senate? Maybe it does," Woods wrote.
If other rumored candidates jumped in the 2020 Senate contest – namely liberal Arizona Congressman Ruben Gallego, who has also floated the idea of a run – Woods' history as a Republican could have become a liability in the primary.
When Hughes asked if he would support a center-right primary challenger to Trump, such as former Ohio governor John Kasich, Woods said that he would. He went on to criticize the leftward movement within the Democratic Party.
"The people who are anti-business, who have these litmus tests that are really far-left – very liberal – that's not where I'm at ... and if that's where the Democratic Party goes, I think it's a big mistake," Woods said. "They can still hand this to Donald Trump."