Senator Lindsey Graham died on Sunday, creating a vacancy that will be filled through a special election in South Carolina.
Within 24 hours, several Republican officials began discussing potential candidacies, prompting criticism from Representative William Timmons.
Timmons said the rapid speculation felt inappropriate and appeared driven by a desire for attention.
Two members of the state's congressional delegation, Representatives Nancy Mace and Ralph Norman, have signaled interest in the August 11 special election.
Mace hinted at a possible run after losing the recent gubernatorial primary, posting a quote from a film on social media.
Norman indicated he is seeking an endorsement from former President Donald Trump, who advised him to take time before deciding.
Timmons, a longtime associate of Graham, questioned whether either candidate could prevail given recent polling data.
He emphasized that the next senator must earn respect and avoid partisan attacks, citing Graham's collaborative approach as a model.
Timmons warned that candidates who rely on extreme statements for media clicks are unlikely to be rewarded by South Carolina voters.
In the interim, Graham's younger sister, Darline Graham, will be sworn in to serve the remainder of the term.
Darline Graham has no prior elected experience and is scheduled to assume office on Tuesday.
The filing period for the primary opens one week after the swearing‑in, and Timmons declined to rule out a future candidacy, noting the president’s influence on the selection.
