On Thursday, Senator Tina Smith of Minnesota took to Twitter to declare her support for ending the filibuster. “The Senate needs to abolish the filibuster. It’s undemocratic,” she wrote, adding, “We need to move this country forward.”

A day earlier, Senator Amy Klobuchar, the state’s senior senator and a standard-bearer for her party’s moderate wing in 2020, said the likely demise in the Senate of a House voting rights bill had flipped her from a “maybe” to a “yes.”

“I would get rid of the filibuster,” Ms. Klobuchar, who chairs the Senate Rules Committee, told Mother Jones magazine. “I have favored filibuster reform for a long time and now especially for this critical election bill.”

Another centrist, Jon Tester of Montana, has taken a wait-and-see approach, but signaled recently that he too might be open to killing the rule.