There are many factors that go into answering this question with any accuracy. They include the length of your stride and your level of endurance, as well as whether you are willing to walk in bad weather.
If you went by Interstate-80 and walked 3MPH continuously, it would take 930 hours (38. 75 days). If you walked 12 hours a day (at 3MPH), it would take 77. 5 days.