WASHINGTON — Senator Rick Scott of Florida, the somewhat embattled head of the Senate Republicans’ campaign arm, said one utterly indisputable thing on Thursday when he stood before a packed auditorium of supporters at the conservative Heritage Foundation: His plan for a G.O.P. majority would make everyone angry at him, Republicans included.

It was an odd admission for the chairman of the National Republican Senatorial Committee. His leader, Senator Mitch McConnell of Kentucky, has repeatedly told Mr. Scott to pipe down about his “11-Point Plan to Rescue America,” with its call to impose income taxes on more than half of Americans who pay none now, and to sunset all legislation after five years, presumably including Social Security and Medicare.

It has divided his party, put Mr. Scott’s own candidates in awkward positions, and is already featured prominently in Democratic advertising. But after Thursday, it is clear the Republicans have not figured out how to address their Rick Scott problem.

“Washington’s full of a bunch of do-nothing people who believe that no conservative idea can ever happen, nothing will change for the better as long as they’re in charge, and that’s why we’re going to get rid of them,” the senator said, ambiguous about who exactly “they” were. “So Republicans are going to complain about the plan. They’ll do it with anonymous quotes, some not so anonymous. They’ll argue that Democrats will use it against us in the election. I hope they do.”

The senator insisted on the Heritage Foundation stage that his plan would raise taxes on no one, only to concede to reporters after the talk that it would — or that it wouldn’t, he couldn’t decide.

“The people that are paying taxes right now — I’m not going to raise their rates; I’ve never done it,” he said, before adding: “I’m focused on the people that can go to work, and decided to be on a government program and not participate in this. I believe whether it’s just a dollar, we all are in this together.”

But most adults who pay no income tax do work, and the plan makes no distinctions. “All Americans should pay some income tax to have skin in the game, even if a small amount. Currently over half of Americans pay no income tax,” it states.

Last year, 57 percent of U.S. households paid no income tax, but that was by design. Successive Republican tax cuts, including President Donald J. Trump’s tax cut of 2017, which greatly expanded the standard deduction, took tens of millions of workers off the income tax rolls, though virtually all of them pay Social Security, Medicare and sales taxes.

And for all of Mr. Scott’s evasions, the criticism is not coming just from the “militant left” that he denounced. The nonpartisan Tax Policy Center estimated that ensuring all households pay at least $100 in income taxes would leave families making about $54,000 or less with more than 80 percent of the tax increase. Those making less than about $100,000 would shoulder 97 percent of the cost.

“Let me tell you what would not be a part of our agenda,” Mr. McConnell told reporters in early March. “We will not have as part of our agenda a bill that raises taxes on half the American people, and sunsets Social Security and Medicare within five years.”

For Democrats, Mr. Scott is a gift. The 2022 campaign is shaping up as a conventional midterm, focused on the economy under Democratic control. That means inflation, gas prices and candidate ties to an unpopular president.

“If you’re in power and you’re presiding over inflation, sorry, it’s tough to be you,” Representative Patrick McHenry, Republican of North Carolina, told The Ripon Society, a conservative research group, this week.

Mr. Scott’s plan has allowed Democrats to talk about the alternative: what Republicans would do with power. Mr. Scott’s plan is chock-full of language about making children say the Pledge of Allegiance, prohibiting the government from asking citizens their race, ethnicity or skin color, and declaring that “men are men, women are women and unborn babies are babies.”

But its economic section has been the focus. Beyond taxing everyone, under the plan, all federal laws would sunset in five years. “If a law is worth keeping, Congress can pass it again,” the plan says. Taken literally, that would leave the fate of Medicare, Medicaid and Social Security to the whims of a Congress that rarely passes anything so expansive.

Democrats are gleefully calling attention to it, even going so far as to promote the Republican senator’s speaking engagement on Thursday.

“The chairman of the National Republican Senatorial Committee has put it on record in a document,” said David Bergstein, a spokesman for the Democratic Senatorial Campaign Committee, “and we are taking his word for it.”

Mr. Scott’s ideas threaten to bring Republicans back to an economic argument they waged — and lost — before Mr. Trump won over wide swaths of white working-class voters with his pledges to leave entitlements alone and cut their taxes.

In 2012, the Republican presidential nominee, Mitt Romney, committed a disastrous gaffe when he was caught on tape describing 47 percent of Americans as wealth takers, not wealth makers.

In 2001, Jim DeMint, a House member from South Carolina at the time, who like Mr. Romney went on to the Senate, asserted that if more than half of Americans paid no taxes, they would vote to expand government largess for themselves and make others pay for it.

“How can a free nation survive when a majority of its citizens, now dependent on government services, no longer have the incentive to restrain the growth of government?” he asked during a Heritage Foundation lecture, calling for all Americans to pay some income taxes.

The vision of affluent Republicans counseling struggling workers to pay more taxes while they pay less was central to Mr. Trump’s critique of the party in the 2016 campaign.

And Mr. Scott is an unlikely bearer of his revanchist message. He’s the richest man in Congress, worth around $260 million, according to the Center for Responsive Politics. In 2002, the sprawling hospital chain he ran agreed to pay more than $880 million to settle the Justice Department’s longest-running inquiry into health care fraud, including $250 million returned to Medicare to resolve charges contested by the government.

Fellow Republicans are not rushing to embrace Mr. Scott’s plan.

“I think it’s good that elected officials put out what they’re for, and so I support his effort to do it,” said Senator Ron Johnson of Wisconsin, among the most endangered Republicans up for re-election in November. “That’s what he’s for.”

But for Republican candidates, the issue is getting awkward. In Arizona, Jim Lamon, a Republican seeking to challenge the Democratic incumbent, Senator Mark Kelly, first called the plan “pretty good stuff” only to have his campaign retreat from that embrace.

Senator Marco Rubio, Republican of Florida, said of the plan, “It’s good that people offer ideas.” His Democratic challenger, Representative Val B. Demings, nevertheless ran an ad on social media accusing him of embracing it.

At a Republican Senate debate in Ohio on Monday, the current front-runner, Mike Gibbons, called the plan “a great first draft in trying to set some things we all believe in,” adding, “The people that don’t believe them probably shouldn’t be Republicans.”

J.D. Vance, a candidate aligned with Mr. Trump’s working-class appeal, fired back: “Why would we increase taxes on the middle class, especially when Apple, Google, Amazon and Facebook pay a lower tax rate than any middle-class American in this room or in this country? It’s ridiculous.”

Even as he denied his plan would do that, Mr. Scott on Thursday was bold in the criticism of his fellow Republicans, whom he is entrusted to help win elections this fall. Timidity is “the kind of old thinking that got us exactly where we are today, where we don’t control the House, the White House or the Senate,” he said, adding: “It’s time to have a plan. It’s time to execute on a plan.”