“Absolutely, it will pass,” Mr. Manchin said of an overhaul of the law, which dictates how Congress formalizes elections.

He said efforts by Mr. Trump and his allies to exploit “ambiguity” in the law were “what caused the insurrection” — the Jan. 6, 2021, attack on the Capitol. That misreading of the statute led to a plan by Mr. Trump and his allies to amass a crowd outside the Capitol to try to pressure Congress and Vice President Mike Pence, who presided over Congress’s official count of electoral votes, to overturn the results of the election.

Ms. Murkowski said the rewrite could be expanded to include other protections for democracy, such as a crackdown on threats and harassment against election workers.

“We want to make sure that if you are going to be an election worker,” Ms. Murkowski said, “you don’t feel intimidated or threatened or harassed.”