Concerns about rising home heating costs are clouding prospects for a proposed tax on methane leaks in the $2 trillion social and climate spending bill backed by President Biden and congressional Democrats.

The tax would charge oil-and-gas producers for leaks of methane from wellheads, pipelines, storage tanks and other facilities. The Congressional Budget Office hasn’t weighed in the financial impact, but independent analysts have said it would cost producers between $1 billion and $10 billion annually.

Methane is a potent greenhouse gas that contributes to global warming. Proponents say the tax would provide incentives for the oil-and-gas industry to plug leaks and capture excess gas that would otherwise be wasted.

Industry groups including the powerful American Petroleum Institute are opposing it, saying the tax is unnecessary given that the Environmental Protection Agency recently proposed new rules to curb methane leaks.

Residential natural-gas prices for August, the most recent available, were up nearly 15% from the same month of 2020, according to the Energy Information Administration. It has forecast that the average U.S. household that relies on natural gas for heating will pay 30% more for the fuel this year.

“The White House’s plan is a recipe for disaster,” said Sen. John Barrasso (R., Wyo.) in a statement. “It will result in skyrocketing power bills, less reliable energy, and fewer jobs for the American people.”

Some gas industry trade groups initially said the levy could raise natural-gas bills by 17%, but they haven’t updated that estimate since lawmakers agreed in September to lower the tax. The nonprofit research group Resources for the Future said the tax would result in a 1% increase in household bills.

Kevin Book, an analyst for ClearView Energy Partners LLC, said there is no reliable way to estimate the costs for consumers because of the number of variables involved.

“It’s certainly a sign of political tone deafness,” Mr. Book said. “And whether or not it’s economically risky, any increase is going to be perceived as a strike against voters, and that would be a weird thing to do politically before closely contested midterms.”