“I think that Vice President Harris herself personifies the need for voting rights to be extended,” the Rev. Al Sharpton, who attended the speech in Tulsa, said in an interview. “When she’s on the phone or walks into an office, we’re looking at the reason we need voting rights.”Michael Waldman, the president of the Brennan Center for Justice at the New York University School of Law, said that the decision to elevate Ms. Harris as the face of the administration’s work on the issue was a pivotal moment for the Biden White House given the number of voter suppression efforts that were moving forward — 389 bills in 48 states and counting, according to a tracker maintained the Brennan Center.“It has been decades since a Democratic White House has made voting rights and democracy reform a central goal,” Mr. Waldman said, but he added, “the clock is ticking.”Ms. Harris’s impact on the hand-to-hand politics of the Senate is expected to be limited, but she often drew attention to voting rights during her four years as a senator. During her last year in the Senate, Ms. Harris introduced legislation that would expand election security measures, require each state to have early in-person voting periods and allow for an expansion of mail-in absentee ballots.In 2020, Ms. Harris was also a co-sponsor of the John Lewis Voting Rights Act, which would restore a piece of the Voting Rights Act of 1965 that relied on a formula to identify states with a history of discrimination and require that those jurisdictions clear any changes to their voting processes with the federal government. The protections were eliminated by the Supreme Court in 2013.Still, Ms. Harris, who spent a chunk of her time in the Senate running for president, was not known for building especially close relationships with colleagues, and Mr. Manchin and Ms. Sinema are no exceptions.Several Democratic aides who work closely with the senators scoffed on Wednesday at the idea that Ms. Harris, known as a staunch liberal, would be the one to persuade either moderate lawmaker to change the filibuster rule. Nor is Ms. Harris a likely candidate to broker the kind of compromise on the substance of the bill needed to persuade Mr. Manchin, the only Democrat who has not sponsored it, to back it.