A Florida con man named Thomas Jefferson Johnson uses the passing of the longtime Congressman from his district, Jeff Johnson (who died of a heart attack while having sex with his secretary), to get elected to the United States Congress as a freshman Congressman, where the money flows from lobbyists. Omitting his first name, and abbreviating his middle name, he calls himself "Jeff" Johnson. He then manages to get on the ballot by pitching a seniors organization, the Silver Foxes, to nominate him as their candidate for office.
Once on the election ballot, he uses the dead Congressman's old campaign material and runs a low budget campaign that appeals to name recognition, figuring most people do not pay much attention and simply vote for the "name you know." He wins a slim victory and is off to Washington, a place where the "streets are lined with gold."
Initially, the lucrative donations and campaign contributions roll in, but as he learns the nature of the con game in Washington D.C., he starts to see how the greed and corruption makes it difficult to address issues such as campaign finance reform, environmental protection, and the possibility that electric power companies may have a product that is giving kids in a small town cancer.
In trying to address these issues, Congressman Johnson finds himself double-crossed by the Chairman of the Committee on Power and Industry, Rep. Dick Dodge. Johnson decides to fight back the only way he knows how: with a con. Johnson succeeds and exposes Dodge as corrupt. As the film ends, it appears likely that Johnson will be thrown out of Congress for the manner in which he was elected, but he defiantly declares, "I'm gonna run for President!" then breaking the fourth wall.

Question: How much of a victory did Thomas have when he ran for Congress?
Answer: very slim
Alternative answer: slim