Cubin worked as a substitute science and math teacher, and was employed full-time as a social worker for senior citizens and disabled adults.

[1] She later worked for the state Labor Department and Ironworkers' Union to train minorities and Vietnam War veterans to become iron workers.

[2] In past elections, Cubin fended off attacks on missed floor votes, which she attributed to her husband's severe health problems.

In July 2005, she suffered a mild heart attack and underwent surgery to place a stent in an artery that was 70 percent blocked.

In November 1994, Cubin ran for Wyoming's U.S. House seat, to succeed Republican Craig Thomas, who was running for (and would be elected to) the United States Senate.

In the wake of the Democratic takeover of Congress in the 2006 elections, Cubin served only on the House Energy and Commerce Committee, as a Member of both the Health and Telecommunications Subcommittees.

[7] In 2006, Cubin was listed as cosponsoring legislation that would sell off some federal land to help pay for Hurricane Katrina and other disaster relief.

About 42 percent of Wyoming's land is owned by the federal government, including Yellowstone and Grand Teton national parks.

[1][9] With regard to global warming, Cubin has stated that "there still exists broad disagreement within the scientific community on the extent to which humans actually contribute to the Earth's temperature changes.

[1] During her time in the House, Cubin rose into the ranks of Republican leadership, holding the posts of Deputy Majority Whip, Conference Secretary, and member of the Steering Committee.

In November 1997, Cubin was one of eighteen House Republicans to co-sponsor a resolution by Bob Barr that sought to launch an impeachment inquiry against President Clinton.

[23] The Wyoming Democratic Party has repeatedly called for Cubin to return the $22,520 she received from Tom DeLay's Americans for a Republican Majority political action committee (ARMPAC).

[24] On July 23, 2006 the Casper Star-Tribune reported Cubin "will keep the money she received from former Rep. Tom DeLay's fundraising committee even though the organization has been fined for campaign finance violations and is shutting down."