The petition began circulating Thursday; as of Wednesday, more than 4,300 people have signed it.
U.S. Rep. Terri Sewell, who is from Selma, was skeptical about the petition, AL.com reported.
“My friend and mentor, Congressman John Lewis, deserves all the praise and recognition for being the beloved civil rights leader that he is," Sewell wrote. "While I understand and respect the movement to rename the bridge in Selma in his honor, I also believe it to be counterproductive. While a magnanimous gesture, such a symbolic effort, at this moment, when John is in the fight of his life, is not what he needs. I urge us all to band together in support of his recovery.
The bridge, built in 1939, was named for Edmund Winston Pettus, a U.S. senator from Alabama who served from 1897 to 1907. He was also a Confederate brigadier general during the Civil War.