Democrats and Republicans remain at odds on how to avoid a round of budget cuts so deep and arbitrary that to allow them now could push the economy back into recession. The cuts, known as a sequester, will kick in March 1 unless Republicans agree to President Obama’s demand to a legislative package that combines spending reductions and tax increases. As of Thursday, with the deadline a week off, Republicans seemed determined to say no to any new tax increases.

“Spending is the problem,” declared the House speaker, John Boehner. “Spending must be the focus.” Reflecting the views of many of her Republican colleagues, Representative Martha Roby said Wednesday that Mr. Obama “already got his tax increase” as part of the January agreement over the “fiscal cliff” and that no further increases were necessary.

Both are wrong. To reduce the deficit in a weak economy, new taxes on high-income Americans are a matter of necessity and fairness; they are also a necessary precondition to what in time will have to be tax increases on the middle class. Contrary to Mr. Boehner’s “spending problem” claim, much of the deficit in the next 10 years can be chalked up to chronic revenue shortfalls from the Bush-era tax cuts, which were only partly undone in the fiscal-cliff deal earlier this year. (Wars and a recession also contributed.) It stands to reason that a deficit caused partly by inadequate revenue must be corrected in part by new taxes. And the only way to raise taxes now without harming the recovery is to impose them on high-income filers, for whom a tax increase is unlikely to cut into spending.

As it happens, those taxpayers are the same ones who benefited most from Bush-era tax breaks and who continue to pay low taxes. Even with recent increases, the new top rate of 39.6 percent is historically low; investment income is still taxed at special low rates; and the heirs of multimillion-dollar estates face lower taxes than at almost any time in modern memory.