President Biden’s highly touted September deal to avert a crippling nationwide railroad strike is slowly unraveling as union leaders attempting to sell the deal to rank-and-file members meet with skepticism and rejection.

Members of a second railroad union, the Brother of Railway Signalmen, have voted to reject a tentative agreement negotiated between union leaders and a railroad industry association. The union said 60 percent of its 6,000 members voted against a deal that promised a 24 percent wage increase, cash bonuses, and caps on health care costs.

“For the first time that I can remember, the BRS members voted not to ratify a National Agreement, and with the highest participation rate in BRS history,” the union’s president, Michael Baldwin, said. Negotiators “failed to recognize the safety-sensitive and highly stressful job BRS members perform each day to keep the railroad running and supply chain flowing.”

The vote is the second this month by union members to reject the earlier agreement. The Brotherhood of Maintenance of Way Employees voted October 10 not to ratify the tentative deal. The rejections lock all the parties into a “status quo” period lasting until November 19, during which negotiations to avert a strike will continue.

All 12 railroad unions representing a total of 115,000 members must ratify the September deal to prevent a shutdown of the network. So far, members of six of those unions have signed off on the deal.

The American Association of Railroads has said that a nationwide strike by rail workers could cripple the American economy and create another supply chain nightmare. It could cost the country as much as $2 billion a day as the movement of goods — and commuters — on roughly 140,000 miles of track comes to a grinding halt.

When the deal was announced September 15, Mr. Biden hailed it as a “big win for America” and showered his labor secretary, Marty Walsh — “a card-carrying union member and the first union labor secretary in decades,” Mr. Biden stressed — with praise for leading marathon, overnight talks that led to the agreement.

“This agreement is validation — validation of what I’ve always believed: Unions and management can work together — can work together for the benefit of everyone,” Mr. Biden said.

The September deal promised railroad employees across-the-board pay increases of 24 percent, along with cash bonuses averaging $11,000 on ratification of the agreement that would bring the average salary in the industry to $110,000 a year. Union members said the deal failed to address longstanding issues such as short staffing, long hours, harsh attendance policies, and a lack of paid time off for medical emergencies.

The White House insists that the threat of a strike remains low and that the cooling-off period should give the parties plenty of time to work out their differences.

“As the president has said for months, any shutdown would be completely unacceptable. It is the responsibility of the parties involved to resolve this issue,” the White House press secretary, Karine Jean Pierre, said Thursday. “These unions’ rejection of the current proposed contract does not mean we face an immediate rail shutdown. That’s not how we view it. But it does mean that the union and the employers have additional work to do.”

After the maintenance workers’ vote, however, representatives of the railroad industry flatly rejected the new demands put forward by union members. “Now is not the time to introduce new demands that rekindle the prospect of a railroad strike,” industry officials said.