The draft plan, which is expected to be unveiled in the coming days, is part of talks over how to salvage pieces of President Biden’s domestic agenda.WASHINGTON — Senate Democrats will push to raise taxes on some high-earning Americans and steer the money to improving the solvency of Medicare, according to officials briefed on the plan, as they cobble together a modest version of President Biden’s stalled tax and spending package.The proposal is projected to raise $203 billion over a decade by imposing an additional 3.8 percent tax on income earned from owning a piece of what is known as a pass-through business, such as a law firm or medical practice. The money that would be generated by the change is estimated to be enough to extend the solvency of the Medicare trust fund that pays for hospital care — currently set to begin running out of money in 2028 — until 2031.It is the most recent agreement to emerge from private negotiations between Senator Chuck Schumer of New York, the majority leader, and Senator Joe Manchin III of West Virginia, a conservative-leaning Democrat who has demanded that his party rein in its sweeping ambitions for a domestic policy plan. In December, Mr. Manchin torpedoed efforts to pass Mr. Biden’s $2.2 trillion social safety net, climate and tax package because of concerns over its cost and impact on the economy at a time of rising inflation.His backing is critical because, with Republicans expected to be uniformly opposed, the only way Democrats can pass the package through the evenly divided Senate is to win unanimous backing from their caucus and do so under special budget rules that would shield it from a filibuster and allow it to pass on a simple majority vote.Mr. Schumer has worked to salvage key components of the plan that could meet that test, including a plan released on Wednesday to lower the cost of prescription drugs. Mr. Manchin has repeatedly said such legislation should focus on tax reform and drug pricing, as well as efforts to lower the national debt. The bill is also expected to include some climate and energy provisions, a key priority for Democrats, although they have yet to be agreed upon.Democratic leaders, who hope to move the legislation through the Senate this month, are expected to formally release the Medicare plan in the coming days, according to the officials, who disclosed preliminary details on the condition of anonymity.The fast-track budget process that the party plans to use for the overall package, known as reconciliation, requires legislation to abide by strict budgetary rules enforced by the Senate parliamentarian. The prescription drug legislation has been submitted to the parliamentarian, and Democrats plan to submit the tax increase and Medicare piece in coming days.The portion of Medicare that pays for hospital bills is funded through a special trust fund, largely financed by payroll taxes. But with escalating health care costs and an aging population, current revenues won’t be enough to pay all of Medicare’s hospital bills forever. According to the most recent report from Medicare’s trustees, the fund will be depleted in 2028 without new revenues or spending cuts.The Democrats’ plan would extend an existing 3.8 percent net investment income tax to so-called pass-through income, earned from businesses that distribute profits to their owners. Many people who work at such firms — such as law partners and hedge fund managers — earn high incomes, but avoid the 3.8 percent tax on the bulk of it.The new proposal would apply only to people earning more than $400,000 a year, and joint filers, trusts and estates bringing in more than $500,000, in accordance with Mr. Biden’s pledge that he would not raise taxes for people who make less than $400,000 a year. The proposal is similar to a tax increase Mr. Biden proposed in 2021 to help offset the cost of a set of new spending programs meant to help workers and families, like home health care and child care.Senator Joe Manchin III has said Democrats should focus on tax reform, prescription drug costs and efforts to lower the national debt.Tom Brenner for The New York TimesImposing the new tax on pass-through income would raise about $202.6 billion over a decade, according to an estimate from the Joint Committee on Taxation provided to Senate Democrats and reviewed by The New York Times. Those funds would be funneled directly into the Hospital Insurance Trust Fund, which covers inpatient hospital care, some home health care and hospice care.The Office of the Actuary in the Centers for Medicare & Medicaid Services informed Democratic staff that the additional revenue generated would extend the hospital trust fund’s solvency from 2028 to 2031.“Medicare is a lifeline for millions of American seniors and Senator Manchin has always supported pathways to ensure it remains solvent,” said Sam Runyon, a spokeswoman for Mr. Manchin. “He remains optimistic there is a path to do just that.”She cautioned that an overall deal on a broader climate, tax and spending package has yet to be struck. Some Democrats also hope to include an extension of expanded Affordable Care Act subsidies, which passed on a party-line vote in the $1.9 trillion pandemic aid package in 2021.“Senator Manchin still has serious unresolved concerns, and there is a lot of work to be done before it’s conceivable that a deal can be reached he can sign onto,” Ms. Runyon said.While Mr. Manchin has said he would support additional tax increases, any changes to the tax code must also win the support of Senator Kyrsten Sinema of Arizona, a centrist who opposed many of her party’s initial tax proposals.And while many Democrats are anxious to address climate change before the midterm elections, which may change the balance of power in Washington, Mr. Manchin, who has been protective of his state’s coal industry, continues to haggle over that issue.The heart of the climate plan is expected to be approximately $300 billion in tax credits to expand the development of clean energy like wind, solar and battery storage, a significantly smaller plan that reflects concessions to Mr. Manchin, according to several people familiar with the negotiations.Negotiators are also considering tax credits to incentivize the purchase of electric vehicles, though it is unclear whether Mr. Manchin will support such a provision.Lisa Friedman More