Yes, it is possible, but there would be no room for unexpected conditions. In Wyoming we had to pedal hard going downhill to get up to 8 mph because of the headwinds. Averaging 116 miles a day for 14 days could be a real challenge. You also won't be taking any time to "smell the roses".

When I was in my early 30's, and in pretty good racing shape, I did an 1100 mile combined tour/training ride in 11 days. I was lightly loaded, but had camping and cooking gear. I averaged 100 miles a day, but it took an 169 mile day to do it. I was probably averaging 250-300 mile training weeks for a couple of months before this venture. There is a difference in being in good shape, and being in good cycling shape. Get a good saddle that fits

Depending on your route, you have a good chance of encountering headwinds, and there are a couple of hills between Oregon and North Dakota.

Give it try, but have a bail out plan just in case things don't go as planned.