For an observer in Omaha, Nebraka, what constellation would the sun appear to occupy on Feb. 1st ?

For a start your position on Earth doesn't matter, it's the same for everybody. Also it won't appear to be in any constellation as you can't see the stars during the day, except during a solar eclipse. If, however, you were beyond the Earth's atmosphere the Sun would appear to be in Capricorn on Feb 1st.