(Otis to near Willamina)
(Valley Jct. to Santiam Jct. except for portions near Rickreall and within Salem)
"Proposed route would begin on U. S. 101 at Otis thence easterly over State Route 18 to Valley Junction thence southeasterly over State Route 22 through Salem, Stayton and Detroit, thence southerly to U. S. 20 at Santiam Junction."
~ AASHO, July 9, 1958 Memo (p. 5 in document, p. 4 in PDF)
According to US-Highways.com, the only US-320 that actually existed was in Wyoming from 1926 to 1939; it now survives as a portion of US-26 and WY-789. However, a post on misc.transport.road reveals that in 1958, Oregon applied to have the US-320 designation run from Otis (near Lincoln City) to Santiam Jct. via Salem. It would've shortened OR-18 to between Willamina and McMinnville at the time (OR-18's eastward extension didn't happen until 1963), but it was OR-22 that would've been drastically shortened to between Hebo and Valley Jct., 18% of its current length. OR-22 itself was extended over that very section in 1952, supplanting OR-14.
Oregon submitted this plan to AASHO in 1958, but it was rejected. The consensus on m.t.r is that it was cancelled because it was an "in-state" US highway, meaning that it did not cross state boundaries. This is evidenced by an AASHO directive around 1964 that urged the decommissioning of all US Highways that were shorter that 300 miles long and did not cross state boundaries (hence the decommissioning of US-126 in 1972). This highway, if approved, would've only gone about 140 miles from coast to Cascades, so it makes sense that so close to the AASHO directive that it was not approved. However, they approved US-126 6 years earlier when US-26 came into Oregon. They didn't specify a reason for denial, so who knows. It is an interesting piece of Oregon highway history, and it makes me wonder what other Oregon US Highways could have been.
If you want to check this out, the AASHO document can be found here. The Oregon information is on page 4 of 5.