Before becoming a cast member of "Saturday Night Live" (1975), Sweeney was hired as a writer. He wrote a number of spec skits and then got them directly into the hands of then-head producer Jean Doumanian by buying buying a bunch of sandwiches and sides from the Carnegie Deli and telling the security guard that he was a delivery man with lunch for the "SNL" offices. Once inside her office, he admitted to Doumanian that he knew she hadn't really ordered the sandwiches, but he gave her the scripts (and the lunch) anyway; about a week later, she called him and offered him a job.

Sweeney told an interviewer for afterelton.com that very few staff writers other than Sweeney himself and Sweeney's boyfriend, Lanier Laney, were interested in writing parts for him on "SNL" (because of their stated hesitance in writing for a gay cast member)--with the exception of Al Franken and Franken's writing partner, Tom Davis. Franken, who was always interested in writing politically themed skits, was the first person who told Sweeney that, due to his resemblance to Ron Reagan Jr., Sweeney should try playing Nancy Reagan in a skit. Playing the then-first lady proved to be Sweeney's most memorable role on "SNL," and Franken eventually parlayed his interest in politics into becoming a US senator from Minnesota.