She taught school in Iowa, Colorado, and in Lusk, Wyoming,[4] and undertook graduate study at the University of Southern California, which awarded her a master's degree in education in 1929.

[3] Polly Cutler's secretarial work took her to the Arizona State Capitol in Phoenix, where she met Representative William "Rosey" Rosenbaum, whom she married in 1939.

She retired from the legislature at the age of 95 after losing the November 1994 election to a political newcomer who benefited from redistricting (which had resulted in her district including parts of eight counties[6]) and an anti-incumbency mood.

Senator Barry Goldwater, an Arizona Republican, told the Los Angeles Times: "People in this state still can't believe she was defeated.... She's so damn good that everybody wanted to see her stay in the Legislature as long as she wanted—and I have a hunch that was where she planned to spend her life.

"[7] As a legislator, Rosenbaum was particularly noted for her efforts on behalf of Arizona's rural areas and her support for education, libraries, museums, and historic preservation.

[7] At the time of her departure from the Arizona legislature at age 95, Rosenbaum was still known for her high energy level, almost always climbing the stairs to her third-floor office instead of using the elevator.

[7] As a volunteer at the Arizona Mining and Mineral Museum, she led guided tours for school groups and was known for her habit of running up the stairs.

After her death, the Arizona Republic said of her in an editorial-page remembrance: "Right up to the end, she kept on giving speeches, serving on committees and even trying to get rose bushes planted in front of the Capitol again.