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Jeb Bush unveiled his tax plan at a factory in Garner, N.C., on Wednesday.Credit Gerry Broome/Associated Press

WASHINGTON — Former Gov. Jeb Bush of Florida challenged some long-held tenets of conservative tax policy on Wednesday by proposing to curtail valuable deductions that benefit the wealthy and eliminate the tax loophole that has benefited hedge fund and private equity managers for years.

That an establishment Republican candidate has embraced such changes not only highlights how income inequality has altered the tenor of the presidential debate for the party, but also indicates the ideological pull Donald J. Trump’s candidacy is having on the Republican field after he made similar proposals.

Mr. Bush’s proposals nevertheless drew a harsh rebuke from Democrats who are unhappy that he is seeking to lower taxes across all income brackets and slash the corporate tax rate. At the same time, conservative anti-tax activists were worried by his suggestion that “carried interest” — the profits that fund managers get from investing other people’s money — should be taxed at a higher rate, like ordinary income.

“No Republican should be for higher taxes on capital gains,” said Ryan Ellis, tax policy director at Americans for Tax Reform. “This tax hike idea is supported by Barack Obama, Hillary Clinton, Bernie Sanders and Elizabeth Warren. The Democratic left deeply wishes to tax all capital gains as ordinary income.”

The debate over how to tax carried interest has become central to a wider battle over income inequality, which Mr. Bush has been highlighting along with other Republican candidates like Mr. Trump and Mike Huckabee as they seek to undercut Democrats on an issue that polls show has increasing resonance with voters. Mitt Romney’s 2012 presidential bid was dogged by the carried interest issue when he revealed that he paid an effective tax rate of about 15 percent, largely on his compensation from Bain Capital.

But the effect of Mr. Bush’s proposals on the wealthy would be muted by his proposal to cut the number of individual tax brackets from seven to three, taxing income at 28 percent, 25 percent and 10 percent. Currently, the top marginal income tax rate is 39.6 percent. His proposals would double the standard tax deduction that most filers take, end what Republicans call the “death tax” on estates of the deceased and seek to make marriage more beneficial for tax purposes.

Mr. Bush’s also proposed cutting the corporate tax rate from 35 percent to 20 percent and giving incentives to invest domestically as he seeks to spur economic growth to an annual rate of 4 percent, an objective that has been met with skepticism by economists.

Speaking from the factory floor of a poultry-chilling-equipment company just south of Raleigh, N.C., Mr. Bush struck a series of populist notes.

“The new normal is a comfortable ride for the affluent people that live off their portfolios,” he told a crowd of supporters and workers with protective goggles resting on their foreheads. “My plan will help those who live on their paychecks, who haven’t seen a raise in a while.”

Other Republican candidates have struck similar themes, with Mr. Huckabee railing against calls to curtail Social Security and Medicare, and Gov. John Kasich of Ohio accepting a Medicaid expansion for his state while speaking of the need to “reach out to the people who live in the shadows, the people who don’t seem to ever think that they get a fair deal.”

Mr. Bush also said he wanted to discourage “corporate inversions” in which American companies use cross-border mergers to take advantage of lower tax rates abroad; he would do so by ending the practice of taxing the international profits of such corporations. He would also assess a one-time tax on corporate money stashed overseas and eliminate the interest deductions that companies take when they borrow, in addition to setting his sights on the sensitive issue of carried interest.

The current system “punishes people for doing things we should encourage and rewards people for doing things that may not be so good,” he said in his appearance Wednesday in North Carolina.

Mr. Bush’s idea of taxing carried interest at his highest proposed rate of 28 percent, rather than at the lower capital gains rate of 23.8 percent, could draw the most consternation from Republicans, making such an overhaul difficult to pass through Congress without bipartisan support. Wall Street donors and lobbyists have fought President Obama’s effort to make such changes, and they were vocal in their opposition on Wednesday.

“Increasing taxes on carried interest would discourage growth and investment and would make our tax code more complex and less fair,” said James Maloney, a spokesman for Private Equity Growth Capital Council, which lobbies for the industry. “Instead of increasing taxes on private equity, venture capital and real estate investment, it is our hope that as the debate over tax reform unfolds, presidential candidates will utilize the opportunity to encourage, not undermine, long-term investment in the United States.”

While Mr. Bush’s plan embraces some of Mr. Trump’s populist language, he also took a subtle jab at his rival, suggesting that the billionaire tycoon has not come forward with a specific proposal to overhaul taxes.

“You have to be willing to take a chance,” he said. “This political environment we’re in now where the louder voices just turn up the volume — that’s a sign of strength and leadership. It isn’t.”

Democrats pounced on Mr. Bush’s proposals on Wednesday as a strategy that would most benefit the rich and impose new costs on the middle class, and they compared his tax cuts to those enacted by his brother, former President George W. Bush.

“More massive tax cuts for the wealthy and corporations, all while exploding the deficit or shifting the burden onto the middle class — an even more extreme plan than his brother’s,” said Holly Shulman, a spokeswoman for the Democratic National Committee.

American Bridge, a Democratic “super PAC,” pointed out that Mr. Bush’s proposals would pose little hardship for hedge fund managers because they would be facing a lower personal income rate anyway.

The effect Mr. Bush’s proposals would have on the deficit remains unclear. A Bush spokeswoman would not say how long he projects it would take to achieve 4 percent economic growth or how the lost tax revenue would be accounted for in the short term.

Roberton Williams, a senior fellow at the nonpartisan Tax Policy Center, said that Mr. Bush’s proposal was similar to the plan that Mitt Romney put forward in 2012 and that it would be a struggle to make such deep tax cuts pay for themselves through faster growth. Cutting the top income rate paid by the richest Americans by nearly a third while ratcheting up standard deductions, he said, will dwarf the effect of closing some loopholes.

“The one thing that seems pretty obvious is that this has to be a big revenue loser,” Mr. Williams said.