It was almost exactly three weeks until Election Day, and Representative Ruben Gallego was tramping his way through the red dust of the Grand Canyon, determined to make it down 3,000 feet to the bottom.

Shortly after Mr. Gallego, a Democrat, announced his Senate campaign last year, he made a promise to visit all 22 of Arizona’s federally recognized tribes — including the Havasupai people, a tribe of 639 people who live in a village nestled below the craggy rim of the canyon.

There are no roads into Supai village, only trails. So on Monday, Mr. Gallego found himself making the four-hour trek on foot, navigating through the earthen curves of the canyon and at one point taking off his hiking boots to traverse a small creek.

The unusual journey in the middle of campaign season underscored the importance of the Indigenous vote in Arizona, which is home to one of the largest Native populations of voting age in the country, and the extreme lengths to which candidates in competitive elections will go to meet voters, quite literally, where they are.

Mr. Gallego is facing off against Kari Lake, a Republican and close ally of former President Donald J. Trump’s, to succeed retiring Senator Kyrsten Sinema, an Independent who is retiring, in a seat that Democrats must hold to maintain their fragile hold on the Senate.