Republican Sen. Bill Cassidy of Louisiana, a former physician who has spent his career touting the safety of vaccines, will likely determine whether Robert F. Kennedy Jr., a vaccine skeptic, becomes the country’s next Health and Human Services secretary.

One Republican, John Fleming, has already jumped in to challenge Cassidy for the party’s Senate nomination next year. Fleming, who served four terms representing a western Louisiana district in the House, cited Cassidy’s impeachment vote in announcing his bid in December.

The fate of Robert F. Kennedy Jr.’s bid to run HHS may rest with a Republican wrestling with his training as a physician and his instincts as a politician.