Mr. Manchin is the only senator on the Democratic side of the chamber who isn’t listed as a co-sponsor of the legislation. Last week he told reporters he was still reviewing it. All 49 other Senate Democrats back the bill, which would loosen state voter-identification requirements, expand mail-in voting and mandate online and same-day voter registration as well as early voting, among other steps.

The top West Virginia election official, Republican Mac Warner, is headed to Washington to testify before the Senate Rules Committee on Wednesday about the legislation, and at least one member of Mr. Manchin’s staff was on a call with state and county officials Monday. Mr. Manchin’s office didn’t respond to requests for comment…

Mr. Warner, West Virginia’s secretary of state, plans to lobby against the bill. He said he has a number of concerns with the legislation, including that it would impose some federal requirements, such as same-day registration, that he said don’t make sense for his state…

On the call Monday, West Virginia election officials voiced concerns about the bill, according to three participants on the call. One of them was Jan Pest, the Democratic county clerk in Marshall County, W.Va. Among other concerns, Mrs. Pest criticized the bill for mandating same-day voter registration, which she worries would invite fraud. Studies have found that voter fraud has been rare.