The White House wants to get a tax bill passed, and on Thursday—just hours before Senate Republicans unveiled the outline of their tax proposal—Gary Cohn, Donald Trump’s top economic adviser, told CNBC’s John Harwood that the President had laid down “two really important principles” to guide the lawmakers and officials putting the legislation together. “Number one is we have to deliver middle-class tax cuts to the hardworking families in this country,” Cohn said. “Number two, our corporate tax system just is not competitive with the rest of the world. We have to create a corporate tax rate, and along with that a pass-through tax rate, that makes us competitive with the rest of the world so we can attract businesses back to the United States.”

Yet since last week, when Paul Ryan and the House Republicans released their tax plan, it’s been clear that Trump’s two principles have run into conflict with each other. Or, rather, these principles have run into the laws of arithmetic, and the fact that there isn’t enough money in the Republicans’ own budget, even using the fuzzy fiscal math the Party favors, to provide big giveaways for all businesses and all households. Something had to give, and between businesses and households, House Republicans went with the businesses.

From what we’ve seen of the Senate bill, so far, it does the same. The proposal follows the basic framework of the Ryan plan: slashing the corporate tax rate from thirty-five per cent to twenty per cent and giving a big tax cut to Donald Trump and other owners of unincorporated businesses. One of the concessions that Republican senators are making to concerns that Democrats and deficit hawks have raised is a one-year delay before implementing the corporate tax cut. Given how big the cut is, corporations will be willing to wait.

We don’t yet have any independent analyses of how the Senate proposal would affect different income groups, but in this aspect, too, it is likely to track with the Ryan bill. According to a new analysis by the nonpartisan Tax Policy Center, the Ryan bill would give taxpayers in the middle twenty per cent of the income distribution in 2018 a tax cut of eight hundred and forty dollars, or $16.15 a week, on average. Compared to the $37,440 break that taxpayers in the top one per cent would receive, that’s not very much. But at least it’s something.

This snapshot of the bill’s effect on the “hardworking families” that Cohn referred to in his CNBC interview, however, is misleading. Over time, the modest tax breaks these people would initially receive would erode—and ten years from now many of them would be paying more money, not less, to the federal government. By 2027, according to other figures contained in the Tax Policy Center’s study, families with children that earn between fifty and seventy-five thousand dollars annually would be subjected to a tax increase of two hundred and thirty dollars a year, or $4.42 a week, on average. Families with children that earn between forty and fifty thousand dollars would face a slightly larger tax increase, of two hundred and forty dollars, or $4.62 a week.

The Times’s David Leonhardt, who also written about some of these figures, suggested a new name for the G.O.P. bill: “Paul Ryan’s 2017 Tax Increase on Middle-Class Families.” Clearly, Ryan or Trump wouldn’t embrace that moniker. But how did they end up with such a proposal, given the principles they claim to have started out with? In answering that question, it is necessary to take account of arithmetic, the Senate’s procedural rules, and the G.O.P.’s desire to pay back its wealthy corporate and individual donors.

To pass a tax bill with just fifty-one votes in the Senate—rather than sixty—the Republicans must keep the over-all cost of their proposal to $1.5 trillion over ten years. Even when allowing for a one-year delay in implementing the corporate tax cut, the business provisions of the G.O.P.’s plans swallow the lion’s share of that sum. According to an analysis of the Senate Republicans’ plan that the Joint Committee on Taxation released on Thursday, cutting the corporate tax rate to twenty per cent starting in 2019 would cost $1.33 trillion by 2027. The Senate’s version of the tax cut for unincorporated businesses, which is somewhat different from the one in the House plan, would cost about $285 billion. If you combine these two items alone, you get to $1.62 trillion—which is already over the $1.5 trillion limit.

To be sure, both the House and the Senate bills include some offsetting revenue raisers on the corporate side, mostly by limiting various types of deductions. But even after accounting for these offsets, the cost of the business tax cuts comes to more than a trillion dollars. That greatly limits the scope for universal tax cuts on the personal side, and so does the G.O.P.’s determination to abolish the Alternative Minimum Tax, which is designed to insure that wealthy people with clever accountants, such as Trump, pay at least some federal taxes. Over ten years, getting rid of the A.M.T. adds another seven hundred billion dollars to the tab.

The business tax cuts and A.M.T. abolition don’t leave any room for ordinary American households to receive substantial tax cuts. Both Republican bills do expand family tax credits and reduce the marginal tax rates that most households would face; but they also claw back a lot of revenue in other ways, some of which are targeted at families. For example, the two bills would replace individual tax exemptions with a standard household exemption of twenty-four thousand dollars a year. For small families, this change could be advantageous, but it would hurt families who have a lot of children (and a lot of exemptions). And the expanded tax credits expire in 2022, which makes them far less valuable. Meanwhile, a new way of calculating inflation would gradually push taxpayers of all kinds into higher tax brackets.

The upshot of all this is that the Republican tax proposals, which Trump has promoted by promising the biggest tax cuts in history, isn’t much of a tax cut at all in the sense that most Americans understand the term. It’s really designed to reduce the tax burden on businesses and wealthy individuals, and it could only be justified if, defying history, it delivered the economy-wide upsurge in G.D.P. growth, capital investment, and wages that the White House has promised, and which Cohn talked about in his interview. The supposed middle-class tax cuts are a fig leaf. And when you lift up the leaf, the truly regressive and deceitful nature of the bill is revealed. Unless the Republicans shift course entirely, nothing can change that.