WASHINGTON — Opposition from a single moderate Democrat to corporate and income tax rate increases has revived efforts in the Senate to draft a tax on carbon dioxide pollution as a way to pay for the Democrats’ proposed $3.5 billion budget bill.

Senator Kyrsten Sinema of Arizona has not advocated a carbon tax, which President Biden and other key Democrats have shied away from as a huge political risk. But her resistance to tax rate increases to pay for the Democrats’ ambitious social policy and climate legislation has set off a scramble for alternatives — at the very least to show her how difficult it would be assemble a package without those rate hikes.

Senator Ron Wyden of Oregon, the chairman of the Senate Finance Committee, confirmed that the Senate majority leader had asked him to craft legislation that would put a price on carbon emissions but to ensure that the policy would respect Mr. Biden’s pledge not to raise taxes on families earning less than $400,000.

That could be done with some kind of rebate or “carbon dividend” during what Mr. Wyden called a “transition” from fossil fuel-powered cars and trucks to zero emission electric vehicles, and from coal- and natural gas-fired electric power plants to renewable energy. Also under consideration: Exempting gasoline from the levy.

“We’ve got a lot of members who care very deeply about this,” Mr. Wyden said, citing Senators Brian Schatz of Hawaii, Sheldon Whitehouse of Rhode Island and Martin Heinrich of New Mexico.

But other senators and Senate aides have confirmed the driver at the moment is Ms. Sinema, the iconoclastic Arizonan whose inscrutable policy positions in an evenly divided Senate can wreak havoc on Democratic plans. She has already said she cannot back a budget plan that spends $3.5 trillion, though she has not said what price tag she can support. Now her position on taxation has Democrats scrambling.

In an interview with The Arizona Republic published on Thursday evening, Ms. Sinema said that climate change was a major concern that drives her approach to the spending bill.

“In Arizona, we’re all too familiar with the impacts of a changing climate … from increasing wildfires to the severe droughts, to shrinking water levels at Lake Mead, damage to critical infrastructure — these are all the things that we’re dealing with in Arizona every day,” she said. “We know that a changing climate costs Arizonans. And right now, we have the opportunity to pass smart policies to address it — looking forward to that.”

Economists have said for decades that a carbon tax, which would make the use of heavily polluting fuels more expensive, is the most effective way to shift the economy away from fossil fuels toward wind, solar and nuclear power, which do not produce the emissions that are heating the planet.

“A price on carbon, such as a carbon tax, provides the economic incentive for the quickest, cheapest and most comprehensive emission reductions across the entire economy,” said Richard Newell, president of Resources for the Future, a nonpartisan energy and environment research organization.

House and Senate leaders and tax writing chairmen agreed that the budget legislation would largely be funded by returning the top income tax rate to 39.6 percent, from the 37 percent level to which President Donald J. Trump lowered it in 2017. They also agree that the corporate income tax rate should rise from 21 percent, also set in 2017.

But, Democrats confirm, at least for the moment, Ms. Sinema is opposing both moves, potentially blowing a significant hole in the finances of a bill to combat climate change, make permanent a generous per-child tax credit, extend prekindergarten and community college to almost all Americans and subsidize child care, among hundreds of other matters.

“Nearly every day for weeks, Kyrsten has been engaged in direct, good-faith discussions with her Senate colleagues, and President Biden and his team,” John LaBombard, her spokesman, said. “Given the size and scope of the proposal — and the lack of detailed legislative language, or even consensus between the Senate and House around several provisions — we are not offering detailed comments on any one proposed piece of the package while those discussions are ongoing.”

Democrats such as Mr. Schatz and Mr. Whitehouse have long promoted a carbon tax, and it has some Republican support. But when a bipartisan group of senators tried to suggest it could pay for a $1 trillion infrastructure bill, the White House balked, fearing that it would harm the middle class.

Politically, the prospect of enacting a carbon tax remains dicey, Mr. Wyden said. Even if middle-class and low-income families are held harmless with rebates, the fear of higher prices for electricity and some goods has sunk other efforts, notably those pushed by Gov. Jay Inslee of Washington, a Democrat.

“We feel very strongly about honoring the president’s pledge to not take steps in excess of $400,000 and I personally have studied what happened in Washington State, one of the bluest states in the country where Jay Inslee tried repeatedly to get a carbon fee or price, and it went down, largely because voters, dealing with transition in the economy, didn’t feel it would make them whole,” Mr. Wyden said. “In other words, they thought that they would be facing costs that were impossible for their family to handle.”

Depending on how it is structured, a tax on carbon pollution could be the single most powerful policy enacted by the United States to tackle climate change.

A recent analysis by Mr. Newell’s staff found that a tax on American carbon dioxide pollution that started at $15 per ton and escalated to $50 per ton by 2030 would cut domestic carbon emissions by about 44 percent from 2005 levels — getting the Biden administration most of the way to its ambitious goal of reducing greenhouse gases by 50 percent from 2005 levels by 2030. It also found that such a program could actually lead to lower, not higher, electricity bills.

A carbon tax could also solve another worrisome problem for Democrats: Under the rules of the Senate, only legislation that strictly qualifies as budget policy may be included in the bill, which is being moved through Congress under a fast-track process known as reconciliation.

A pollution tax would easily pass that test. An analysis by the Senate Finance Committee found that a carbon tax could raise $500 billion, although under the program envisioned by Democratic leaders, a chunk of that money would be returned to individuals in the form of rebates.

As she has done for weeks, Ms. Sinema refused to comment on continuing negotiations. When one senator asked what revenue measures she would accept, he said he came away believing she could go along with a tax on carbon emissions and a tax on goods from countries that were not clamping down on climate change.

The latter tax, which is backed by Mr. Wyden, would be designed to ensure that other countries with lax environmental rules would not be able to sell their goods at a lower price to American consumers and reap a competitive advantage. Under the rules of the World Trade Organization, it could be difficult for the United States to impose such an import tax — essentially, a tariff on goods from heavily polluting countries — unless its own industries are also subject to one.

Mr. Wyden’s staff members, who are now writing that language, are considering a domestic carbon tax that could start at $15 to $18 per ton, and that would increase over time, according to two people familiar with the matter who were not authorized to speak on the record. The tax would be applied directly to coal mining companies, large natural gas processing plants and oil refiners, based on the emissions associated with their products, with one exception: Oil refiners would very likely be charged for producing diesel fuel and petrochemicals, but not gasoline — a way to try to prevent cost increases from hitting most American drivers at the pump.

But even if they can win Ms. Sinema over to the plan, others may not agree. Democrats still feel the sting of former President Barack Obama’s failed effort to pass a climate change bill that would have forced polluters to pay a fee for their fossil fuel emissions. After the House passed it in 2009, Republicans campaigned against it as an “energy tax.” The bill failed in the Senate and contributed to Democrats’ loss of the House in 2010.

Climate activists are trying to make the case to Ms. Sinema that times, and climate politics, have changed. “I can tell you that our volunteers have placed 1,444 calls and emails to Arizona Senate and House offices in the last few months,” wrote Steve Valk, a spokesman for the Citizens’ Climate Lobby, which wants a price placed on carbon pollution.

A crucial test of whether Ms. Sinema would support a carbon tax would be its effects on Arizona’s economy. Her state has suffered record droughts, which scientists say have been worsened by climate change — and is home to a growing solar power industry.

Robert Aiken, the vice president of federal affairs at Pinnacle West Capital, a Phoenix-based company that owns the largest electric utility in Arizona, said that he spoke on n Thursday with a staff member from an Arizona congressional office about a possible carbon tax provision in the budget bill.

“We were just asked about it from Capitol Hill an hour ago, for the first time,” he said on Thursday afternoon. He said that the company couldn’t yet say whether it would support the legislation until it had closely analyzed the details.

“But there’s no question we are decarbonizing in Arizona,” he said. “We’re headed in that direction. We are at the forefront of decarbonization.”

Jonathan Martin contributed reporting.