The fair place to meet is Las Vegas, NV — the city closest to the midpoint of Portland and Tucson. From the farther side that’s about 15 hr 51 min of driving.
Recommended midpoint
Las Vegas, NV
From Portland
15 hr 51 min
756 mi to Las Vegas
From Tucson
7 hr 35 min
362 mi to Las Vegas
Tucson has the shorter trip; the split is off by about 8 hr 16 min. The alternatives below can even it out. Portland and Tucson are about 1,111 miles apart.
Portland and Tucson are about 1,111 miles apart by road. Split the difference and you arrive near Las Vegas, the city closest to the halfway point between them. That puts roughly 15 hr 51 min of driving on the Portland side and 7 hr 35 min on the Tucson side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Las Vegas still makes a fair, central place for Portland and Tucson to converge, splitting the travel instead of asking one side to cross the country.
If Las Vegas doesn't have what you're after, Sacramento and Salt Lake City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Portland and Tucson.
Las Vegas, colloquially shortened to Vegas, is the most populous city in the U.S. state of Nevada and the county seat of Clark County. It is the 24th-most populous city in the United States, with 641,903 residents at the 2020 census. Read more →
Portland is the most populous city in the U.S. state of Oregon. Located in the Pacific Northwest at the confluence of the Willamette and Columbia rivers, it is the 28th-most populous city in the United States, sixth-most populous on the West Coast, and… Read more →
Tucson is the county seat of and the most populated city in Pima County, Arizona, United States. Read more →
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.
Estimates use straight-line distance and typical road speeds; real drive times vary with route and traffic.