He ran for the United States House of Representatives in the Omaha-based 2nd congressional district in 1978, losing to incumbent Democrat John J. Cavanaugh III.

Cavanaugh declined to run for re-election in 1980 and Daub ran for the seat again, defeating Democrat Richard Fellman.

Senator Edward Zorinsky, a Democrat, died of a heart attack and Governor Kay A. Orr appointed businessman David Karnes to fill the seat.

Morgan, and was narrowly elected to a full term in 1997, both times defeating city councilwoman Brenda Council.

In 2007, Daub briefly ran for the U.S. Senate seat being vacated by Senator Chuck Hagel; he exited the race to offer an early endorsement to Mike Johanns, former Nebraska governor and USDA secretary, who won the seat.

In the April 2009 primary, he received the most votes;[7] however, in the May 2009 runoff election, he lost to Jim Suttle, with unofficial final results of 48.7% to 50.7%.

Daub served for five years on the board of Omaha's Metropolitan Entertainment and Convention Authority (MECA).

[10] As a University regent, Daub called for football players to be removed from the Nebraska Cornhuskers because they knelt during the national anthem in 2017 as a protest against police violence.