His governing style was one of no-nonsense. The best example was shown at the very beginning of his governorship: Upon taking office, Osborn had the state's top officials turn in a signed, but undated, resignation letter. If an official became an embarrassment to the state, Osborn would date the letter, and announce the official had resigned.
During his fourth term, Osborn suffered from Lou Gehrig's Disease and was barely able to communicate with his staff. He eventually died while in office. Osborn was succeeded by Dan Garvey.