It’s an ingenious plan, even elegant in a wonky way. To help fund health care for the estimated 47 million uninsured Americans, budget chief Peter Orszag has proposed changing how the nation’s wealthiest claim income-tax deductions.

The top federal income-tax rate for high earners is 35 percent, and when they claim deductions for mortgage interest, local taxes, or charitable contributions, they can do so at that same 35 percent rate. A $1,000 contribution to a charity saves $350 in taxes, in other words.

But under Orszag’s proposal, the top deductibility rate would be reduced to 28 percent, meaning the same taxpayer would save only $280 — and the federal government would keep the $70 difference. The tax hike would hit only around 1 percent of the nation’s taxpayers and would raise a good chunk of the money needed to launch a health-care plan. And as President Obama points out, the 28 percent rate is the same rate at which wealthy Americans could deduct during the Reagan administration.

But if Orszag’s economic calculation was sound, the administration’s political calculation was not.

Charities have been more divided on the issue. Some have protested that the plan would harm their revenue at a time when the recession already has dampened giving; others have said they wanted to weigh those costs against the benefits of health-care reform.

Republicans in Congress, meanwhile, saw an easy opportunity to slam Obama for trying to raise taxes on civic virtue.

“Who thinks it’s a good idea to cut back on charitable activities?” demanded Eric Cantor, R-Va., the House Republican whip.

Former House Speaker Newt Gingrich, who’s thinking about running for president, accused Obama of declaring “war against churches and charities.”

The fear of looking uncharitable also caused many Democrats to run for the hills. Senate Finance Committee Chairman Max Baucus, D-Mont., who’s in charge of tax legislation, has said he doesn’t like the idea. Senate Budget Committee Chairman Kent Conrad, D-N.D., stripped it out of the budget. Even Rep. Charles Rangel, D-N.Y., normally a stalwart supporter of higher taxes on the rich, said he would have to take a long look at this one.

Where did the White House go wrong? For one thing, the administration unveiled its proposal without selling it first. Members of Congress — including Democrats — were surprised by the idea, and Congress doesn’t like to be surprised. There was also little visible public support. Tweaking the rate at which high-income taxpayers can claim tax deductions is a complicated and (for most people) unfamiliar idea; it takes some explaining.

By the time Obama and his aides had begun to defend the proposal, their Republican opponents already had painted it as an attack on charity. Obama bristles whenever anyone asks whether he is trying to do too much, too soon. But that seems clearly to be the case here: The administration made a proposal that it didn’t have time to explain, and it lost ground as a result.

The administration should have known what was coming. Any tax increase — even on 1 percent of the population — is guaranteed to run into organized opposition. Republicans in Congress aren’t always sure what they’re for these days, but they all know what they’re against: taxes.

Still, the administration should persist in promoting what is basically a sound plan. Obama needs to go back to Congress and explain his reasoning. A recent Gallup poll found that 60 percent of the public agrees with the president that higher-income people should pay more taxes. Obama should use that support in making his case.

A tax break to encourage charitable contributions is reasonable public policy, but there’s nothing sacred about tying it to the marginal tax rate. As Obama likes to say, there’s no clear reason Bill Gates should receive a $350 tax benefit for a $1,000 contribution when lower-income taxpayers making the same donation recoup $150.

As to the charge that he’s harming charities: Yes, reducing deductibility would probably would depress charitable contributions — economists have offered varying estimates of the effect, from approximately 2 percent to perhaps 4 percent — but that doesn’t mean it’s a bad idea. The cost should be weighed against the benefit of health reform.

As to the mortgage-interest deduction, it shouldn’t be considered sacred, either. The real-estate industry portrays the deduction as a way of encouraging homeownership, but there’s no real evidence it works that way. Its benefit isn’t targeted at first-time home buyers or homeowners in general; instead, it goes mainly to upper-income buyers who take on big mortgages. (And aren’t big mortgages one of the reasons we’re in this mess?) Only about half the nation’s homeowners claim the deduction. The rest either have paid off their mortgages or take the standard deduction.

Raising taxes on anyone, even the top 1 percent, is hard work. Just ask George H.W. Bush or Bill Clinton. Obama has made a start. He may not prevail on the first try, but it’s an argument worth making.