"Hillary claiming that as First Lady she "had to work" with Democrats and Republicans is a ludicrous statement."
Actually not a ludicrous statement, and likely one of her few truthful statements. Because remember what Bill appointed her to do as first lady...
Chair the closed-door Task Force on National Health Care Reform, which eventually proposed Hillarycare, or the Health Security Act, as it was formally known. Members of the panel included over 100 people who were employees of members of Congress, Republican and Democrat both. As chair of the task force she also met with many members of Congress and testified extensively on the act.
So, yeah. She worked rather extensively with, and against, both Democrats and Republicans and their representatives as First Lady.