WASHINGTON — House Democrats on Monday presented a plan to pay for their expansive social policy and climate change package by raising taxes by more than $2 trillion, largely on wealthy individuals and profitable corporations.

But the proposal, while substantial in scope, stopped well short of changes needed to dent the vast fortunes of tycoons like Jeff Bezos and Elon Musk, or to thoroughly close the most egregious loopholes exploited by high-flying captains of finance. It aimed to go after the merely rich more than the fabulously rich.

Facing the delicate politics of a narrowly divided Congress, senior House Democrats opted to be more mindful of moderate concerns in their party than of its progressive ambitions. They focused on traditional ways of raising revenue: by raising tax rates on income rather than targeting wealth itself.

Representative Dan Kildee of Michigan, a Democrat on the Ways and Means Committee, which crafted the plan, called it “the boldest common denominator.”

“Being for something doesn’t make it law; 218 votes in the House, 50 votes in the Senate and the president’s signature make it law,” he said, adding, “What I don’t want is another noble defeat.”

The proposal includes nearly $2.1 trillion in increased tax revenues, the nonpartisan Joint Committee on Taxation estimated on Monday. Democrats say those increases will go a long way to funding President Biden’s ambitions to expand the federal government’s role in education, health care, climate change, paid leave and more.

But the bill dispenses of measures floated by the White House and Senate Democrats to tax wealth or to close off avenues that the superrich have exploited to pass on a lifetime of gains to their heirs tax-free.

“It would be a monumental mistake for Congress to pass a bill that really exempts billionaires,” said Senator Ron Wyden of Oregon, the Democratic chairman of the Finance Committee.

Key Democrats cautioned on Monday that the House proposal was likely to change — perhaps considerably — as Mr. Biden’s economic agenda wends its way through the House and Senate, where Democrats hold slim majorities and must hold nearly every member of their ideologically diverse caucus together. But White House officials welcomed the Ways and Means plan and said it took important steps toward the president’s vision of a tax code that rewards ordinary workers at the expense of the very rich.

The proposal includes substantial measures to raise taxes on the rich. Taxable income over $450,000 — or $400,000 for unmarried individuals — would be taxed at 39.6 percent, the top rate before President Donald J. Trump’s 2017 tax cut brought it to 37 percent. The top capital gains rate would rise to 25 percent from 20 percent, considerably less than a White House proposal that would have taxed investment gains as income for the richest, at 39.6 percent.

Under the committee’s plan, a 3 percent surtax would be applied to incomes over $5 million.

The proposal would also raise taxes in a variety of ways on businesses called pass-through entities — like many law firms and financial companies — that distribute profits to their owners, who then pay individual income taxes on them. Those changes, including the extension of an existing 3.8 percent surtax to include pass-through income, would raise taxes primarily on high earners, generating several hundred billion dollars in revenues, by Democratic estimates.

The joint committee estimated on Monday that the changes would raise about $1 trillion from high-income individuals.

Republicans balked at the proposal. Business lobbying groups rejected the package, with the U.S. Chamber of Commerce slamming it as “an existential threat to America’s fragile economic recovery and future prosperity.”

“President Biden, Speaker Nancy Pelosi and House Democrats are ramming through trillions of wasteful spending and crippling tax hikes that will drive prices up even higher, kill millions of American jobs and drive them overseas, and usher in a new era of government dependency with the greatest expansion of the welfare state in our lifetimes,” Representative Kevin Brady of Texas, the committee’s ranking Republican, said of the plan.

But what is not included is notable. The richest of the rich earn little from actual paychecks (Mr. Bezos’s salary as the founder of Amazon was $81,840 in 2020), so a surtax on income would have little impact. Their vast fortunes in stocks, bonds, real estate and other assets grow largely untaxed each year.

“The proposal is extremely modest in the area of structural change,” said Eric Toder, a co-director of the nonpartisan Tax Policy Center in Washington. “Mostly, it is about raising rates on existing tax bases.”

In the Senate, Democrats are taking aim directly at accumulated wealth. The Finance Committee has proposed a one-time surtax on billionaires’ fortunes, followed by annual levies on the gains in value of billionaires’ assets, similar to the way property taxes are adjusted each year to reflect gains in housing values.

Mr. Biden’s expansive tax proposals, during his campaign and as president, did not include a wealth tax. But he and top senators had called for a variety of measures to more heavily tax inherited wealth and the investments of very high earners.

Representative Bill Pascrell Jr. of New Jersey, a Democrat on the Ways and Means Committee, conceded on Monday that large swaths of wealth in the country were tied up in assets, not large salaries. But he said many Democrats were leery of going too far.

“I am very suspect of a wealth tax,” he said. “I think it’s perceived as ‘soak the rich.’ I don’t think it is, but that’s how it’s perceived.”

The committee did take aim at a loophole in retirement savings exploited by the billionaire Peter Thiel, who, according to a ProPublica investigation, was able to take a Roth individual retirement account worth less than $2,000 in 1999 and grow it to $5 billion, which could be completely shielded from taxation.

To prevent such exploitation, the Ways and Means Committee would stop contributions to retirement accounts once they reach $10 million.

In other areas, the committee appears to be making only glancing blows at the wealthiest Americans. Former President Barack Obama, Mr. Trump and Mr. Biden have all vowed to close the so-called carried interest loophole, in which private equity managers pay low capital gains taxes on the fees they charge clients, asserting that the money is not income because it is drawn from their clients’ investment gains.

Senate Democrats have proposed closing the loophole completely, saving Treasury $63 billion over 10 years. The House proposal would merely limit the practice, forcing Wall Street financiers to hold their clients’ investment gains for five years before claiming them as capital gains and cashing out. It would save $14 billion, a fraction of the Senate proposal.

Another item missing from the House plan: a measure to tax inheritances more aggressively. Mr. Biden and many other Democrats want assets such as stocks and real estate to be taxed when they are inherited by wealthy heirs, based on the gain in value from the time the original owner purchased them. Under current law, such assets face capital gains taxation only when they are sold, according to their worth when they were inherited,allowing all the gain in value over the lifetimes of the superwealthy to go untaxed as long as they are passed on to heirs.

But the new proposal faced a fierce lobbying campaign, led by rural Democrats like former Senators Heidi Heitkamp of North Dakota and Max Baucus of Montana. Representative Richard E. Neal of Massachusetts, the Democratic chairman of the Ways and Means Committee, left it out.

To some liberals, Mr. Neal’s pragmatism felt more like surrender.

“America’s billionaires are popping Champagne tonight as the House Ways and Means Committee — led by Chair Richie Neal — fails the president, fails the country and fails history,” said Erica Payne, the president of Patriotic Millionaires, a group of wealthy liberals that embraces much higher taxes on the rich.

Some Democrats expressed surprise on Monday at Mr. Neal’s political calculations.

“A wealth tax? I don’t know anyone who says that’s not working for them politically,” said Representative Donald S. Beyer Jr., Democrat of Virginia and a member of the committee.

But with Senator Joe Manchin III, Democrat of West Virginia, suggesting that the final package might have to be half the size of the House plan, Mr. Beyer said he understood why Democratic leaders did not want to make vulnerable lawmakers embrace the most aggressive options.

“People will be saying, ‘You raised our taxes by $2.9 trillion,’” Mr. Beyer said. “Pelosi and leadership do not want to put a lot of threatened members on anything that’s just going to die in the Senate.”

White House officials on Monday welcomed the House plan, while acknowledging that it was far from a final product.

“We see it as a first step,” said Karine Jean-Pierre, the deputy White House press secretary.

Zolan Kanno-Youngs contributed reporting.